Optical Field Transformation Methods and Systems

ABSTRACT

A method of performing coherent transformations of optical fields includes forming a far field distribution of the input optical field. A fraction of the formed far field is diffracted by producing localized discontinuities within said far field. A Fraunhofer diffraction pattern of the diffracted optical field is formed. The Fraunhofer diffraction pattern is modified by producing localized optical path differences within the Fraunhofer diffraction pattern. The transformed output optical field is produced in the far field with respect to the modified Fraunhofer diffraction pattern.

I. FIELD OF THE INVENTION

The present invention relates to methods and systems employed formodification of optical fields. More specifically, it relates to methodsand systems for transforming the shape and size of optical fielddistributions produced by optical systems.

II. BACKGROUND OF THE INVENTION

One of the most fundamental characteristics of imaging optical systemsis the ability to produce sharp images of objects and to resolve finedetails within these objects. On the other hand, non-imaging opticalsystems are often required to produce various output light patterns bytransforming the propagating radiation. In several photonicsapplications, for example, it is required to produce high peakirradiance or radiance optical fields with complex, spatially structuredradiation patterns.

An optical system's response to a point source, known as thepoint-spread function (PSF) of the optical system, represents one of themost fundamental characteristics of the optical system. The PSF definesa system's ability to form sharp images or to focus the propagatingradiation. The PSF also influences radiance distributions produced byoptical systems in the far field. An image of an object produced by anoptical system is defined as the convolution of an ideal image with thePSF of the optical system producing the image. The PSF size depends onthe radiation wavefront distortions incurred during propagation,including atmospheric effects, optical system aberrations, anddiffraction of the radiation as it propagates through the opticalsystem. In the case of optical systems well corrected for aberrations,the shape and size of the PSF is defined only by obscurations anddiffraction effects on the system's apertures. Optical systems wellcorrected for aberrations are termed as “diffraction-limited.”Diffraction effects limit the resolution of optical systems and preventpropagating radiation from being focused into infinitely small spotswith infinitely high power densities.

When an object is located at infinity, a diffraction-limited opticalsystem with a circular pupil aperture will produce a focused fielddistribution known as an Airy distribution in its back focal plane. TheAiry distribution consists of a high intensity circular central nodesurrounded by lower intensity rings caused by diffraction on the pupilaperture. FIG. 1 shows a normalized intensity cross-section of an Airydistribution. The size of the central node of an Airy distribution,referred to as an Airy disk, depends on the wavelength λ of thepropagating radiation, the aperture diameter D, and the focal length fof the focusing optics. The Airy disk diameter is defined as:

$\begin{matrix}{d_{Airy} = {{2.44\frac{\lambda \; f}{D}} = {2.44\lambda \; N}}} & (1)\end{matrix}$

where the ratio N=f/D is referred to in literature as the f-number of anoptical system. The Airy disk contains about 84% of the propagatingradiation power, while the remaining 16% of the radiation power isdistributed between the lower intensity rings of the Airy distributioncaused by diffraction of the radiation on the circular system aperture.Equation (1) also describes the central node size of a focused fielddistribution from a top-hat-shaped collimated laser beam with diameter Dand wavelength λ produced in the focal plane of a diffraction-limitedfocusing optical system with focal length f.

Amplitude transmission masks and phase masks were employed in the pastto alter the size and shape of PSFs. FIG. 2 presents changes in the PSFcentral node diameter, the power outside of the central node, and thepower contained in the central node for optical systems with centralobscurations produced by opaque, axially-symmetric amplitude maskslocated at the pupil of the optical system. An increase in pupilobscuration by the amplitude mask leads to a reduction in the outputfield central node diameter, but at the same time causes an increase inthe fractional power diffracted outside of the central node and anassociated reduction in the fractional power contained in the centralnode. Pupil obscurations are produced, for example, by secondary mirrorsin reflective telescopes, and result in PSFs with reduced central nodewidths and an increased amount of radiation diffracted outside of thecentral nodes.

The idea of using amplitude masks located at the pupil of an opticalsystem to reduce the Airy disk width was first proposed by Toraldo diFrancia in 1952. Since then, it has been demonstrated that amplitude andphase masks placed at the pupil of an optical system alter the system'sPSF. Several examples of PSF distributions produced with the aid ofamplitude and phase masks have been discussed in the past.

The optical path difference (OPD) introduced by phase mask structures isusually chosen to be equal to an odd integer j of half the wavelength0.5λ of the propagating radiation:

OPD=j0.5λ  (2)

In many cases, the lowest integer value j=1 is employed, and the opticalpath difference introduced by the phase masks equals half the wavelengthof the propagating radiation.

The employment of amplitude or phase masks to shape the PSF of anoptical system is usually associated with a reduction in the fractionalpower contained within the PSF central node and the associated increasein fractional power contained outside of the PSF central node. It waspreviously shown that a reduction in the central node width isassociated with a reduction in the fractional amount of power containedwithin the central node of a focused laser beam and with a respectiveincrease in the fractional amount of power contained within the ringsoutside of the central node.

FIG. 3 presents the relative changes in PSF cross-sections for an Airydistribution, as well as for an optical system containing a pupilsingle-step phase mask with four different radial sizes of the phasezone. The ratio of the PSF peak intensity of an optical system employingamplitude or phase masks to the peak intensity of the Airy distributionis known as the Strehl ratio. FIG. 4 presents the calculated Strehlratios for optical systems with amplitude and phase masks located at thesystem's pupils as a function of the masks' radial sizes. The figureindicates that the use of amplitude or phase masks to alter the PSFshape leads to reduced Strehl ratios. The reduction in Strehl ratio is,in turn, associated with the reduction in the fraction of radiationcontained within the PSF central node and the respective increase in thefraction of the radiation contained outside of the PSF central node.

FIG. 5 presents a circular-shaped uniformly illuminated aperture of adiffraction-limited optical system. FIG. 6 presents the correspondingthree-dimensional shape of the Airy PSF intensity distribution in theback focal plane of the diffraction-limited optical system using theaperture from FIG. 5.

Optical systems with central obscurations are widely employed inreflective telescopes and result in PSFs containing diminished fractionsof radiation within the PSF central node, as was shown in FIG. 2. FIG. 7presents a doughnut-shaped uniformly illuminated aperture of an opticalsystem with central obscuration. The radial size of the obscurationshown in FIG. 7 is about 60% of the aperture radius. FIG. 8 presents athree-dimensional shape of the PSF intensity distribution in the backfocal plane of the optical system with central obscuration. The PSF ofthe system consists of a higher peak intensity central node surroundedby lower intensity rings caused by diffraction of the radiation on thedoughnut-shaped system aperture. The PSF shown in FIG. 8 has a Strehlratio of 0.41. The PSF contains 37.3% of the radiation within thecentral node, while 62.7% of the radiation is diffracted outside of thecentral node and is contained within the rings of the PSF.

Optical systems with distributed apertures are composed of severalspaced apart sub-apertures comprising the system's aperture, and arecapable of producing PSF distributions with central node widths smallerthan the central node widths of PSFs from individual sub-apertures. FIG.9 presents the pupil of an optical system containing 6 distributedapertures. The individual apertures of the optical system in FIG. 9 arenumbered clock-wise in ascending order. The PSF of an optical systemwith 6 distributed apertures shown in FIG. 9 consists of a higher peakintensity central node surrounded by a number of secondary lowerintensity peaks caused by the diffraction of propagating radiation bythe apertures, and is presented in FIG. 10. The PSF of the opticalsystem with distributed apertures has a Strehl ratio of 0.31, andcontains only about 20.7% of the propagating radiation within thecentral node, while 79.3% of the radiation is spread outside of thecentral node of the PSF. The central node width of the PSF in FIG. 10 isabout 5.4 times narrower than the PSF central node widths of theindividual sub-apertures comprising the system.

The fractional radiation content within the central node of a PSFproduced by an optical system is further reduced if the propagatingradiation encounters wavefront distortions. In the case of the opticalsystems with distributed apertures, the fractional power containedwithin the PSF central node will be reduced in the presence of wavefrontdistortions within the individual sub-apertures of the optical system,or when the OPD between the sub-apertures is not equal to an integernumber of the radiation wavelength.

FIGS. 11 and 12 present PSFs of the optical system containing 6distributed sub-apertures in the presence of wavefront distortionsproducing random OPDs between the individual sub-apertures. The PSFshown in FIG. 11 corresponds to a random set of OPDs ranging from −0.14λto 0.15λ and listed as OPD set #1 in the second row of Table 1, where λis the wavelength of the propagating radiation. The PSF in FIG. 11 had aStrehl ratio of 0.22 and contained 17.7% of the total radiation powerwithin the area occupied by the central node of the undistorted PSF. ThePSF shown in FIG. 12 corresponds to a second set of phase errorscorresponding to random OPD set #2 and ranging from −0.35λ to 0.21λ. OPDset #2 is shown in the third row of Table 1. The presence of theserandom phase errors between the individual sub-apertures resulted in afield distribution with a Strehl ratio of 0.16 containing only 12.9% ofthe total radiation power within the area occupied by the central nodeof the undistorted PSF.

TABLE 1 Aperture Number 1 2 3 4 5 6 OPD Set #1 (λ) −0.11 0.15 −0.06 0.020.07 −0.14 OPD Set #2 (λ) −0.19 0.10 0.21 0.17 −0.35 −0.05

A combination of multiple coherent laser beams into an array, known asan Optical Phased Array (OPA), results in a far field distribution witha central node size significantly smaller than the far field centralnodes produced by the individual laser beams. This reduction in the OPAfar field central node size is achieved at the penalty of a significantreduction in the fractional radiation power contained within the OPAcentral node.

The far field distributions are produced at distances L from the OPAthat satisfy the far field condition:

$L > \frac{2\left( D_{OPA} \right)^{2}}{\lambda}$

where λ is the OPA wavelength, and D_(OPA) is the OPA aperture diameter.Alternatively, the far field distributions can be produced in the focalplane of a lens. OPAs may contain different numbers of individual laserbeams and may be arranged into different patterns, with the individualbeams taking different sizes and shapes, including Gaussian,super-Gaussian, top-hat, etc. FIG. 13 shows the near field intensitydistribution produced by an OPA containing seven Gaussian-shapedcoherent laser beams arranged in a circular-symmetric pattern. Theindividual OPA beams are sequentially labeled 1 through 7, as shown inthe figure. FIG. 14 presents the far field irradiance distributionproduced by the OPA in the absence of wavefront distortions and phaseerrors between the laser beams. The far field pattern shown in FIG. 14contains within the central node about 56% of the total OPA power andhas a Strehl ratio of 0.56.

In the presence of wavefront distortions or OPDs between the individuallaser beams within the array, the fractional OPA power contained withinthe central node of the far field is reduced. FIG. 15 presents the farfield from the OPA in the presence of random OPDs between the individualbeams within the array ranging from −0.35λ to 0.21λ. The specific OPDsassociated with the individual OPA laser beams are shown in the secondrow of Table 2. The far field in FIG. 15 has the peak value reduced to0.53 of the respective peak value of the far field containing no phaseerrors. The far field in the presence of the phase errors has a Strehlratio of 0.30 and contains only 37% of the total radiation power withinthe central node.

TABLE 2 Beam Number 1 2 3 4 5 6 7 OPDs (λ) −0.08 −0.19 0.10 0.21 0.17−0.35 −0.05

III. SUMMARY OF THE INVENTION

In accordance with one aspect of the invention, optical fieldtransformation techniques are provided that can alter the shape and sizeof PSFs produced by optical systems, as well as the shape and size ofthe far field distributions produced by laser beams and theircombinations.

In accordance with another aspect of the invention, optical fieldtransformation techniques are provided that can redistribute fractionalpower within the central nodes of PSFs or optical far fielddistributions.

In accordance with still another aspect of the invention, optical fieldtransformation techniques are provided that can redistribute theradiation between the central node and the side-lobes of PSFs or opticalfar field distributions.

In accordance with still another aspect of the invention, optical fieldtransformation techniques are provided that can increase the peakintensity of the central nodes of PSFs or optical far fielddistributions.

In accordance with still another aspect of the invention, optical fieldtransformation techniques are provided that can increase the fraction ofthe propagating radiation contained within the central nodes of PSFs ofoptical far field distributions.

In accordance with still another aspect of the invention, optical fieldtransformation techniques are provided that can increase the peakintensity of central nodes of PSFs or optical far field distributions inthe presence of wavefront distortions of the incoming optical radiation.

In accordance with still another aspect of the invention, optical fieldtransformation techniques are provided that can increase the fraction ofthe propagating radiation contained within the central nodes of PSFs oroptical far field distributions in the presence of wavefront distortionsof the incoming optical radiation.

In accordance with still another aspect of the invention, optical fieldtransformation techniques are provided that can reduce distortions ofthe incoming optical radiation.

In accordance with still another aspect of the invention, opticalsystems are provided for implementation of the above identified opticalfield transformation techniques.

In accordance with the present invention, the optical fields aresubjected to optical transformations resulting in the formation ofmodified fields that satisfy the above identified aspects. By anappropriate selection of the optical properties of components employedduring the field transformations, significant flexibility in changingthe shape, size, fractional power, and peak intensity of the centralnode of the optical far field is realized. For example, during the fieldtransformations in accordance with the present invention, a variety ofdifferent shapes and sizes of the transformed output field can beachieved,

The aspects of the present invention are achieved in accordance withimplementation techniques and design examples, as will be explained indetail in the following embodiments.

The features of the present invention, including the construction andoperational details of the preferred embodiments, will now be describedwith reference to the accompanying drawings.

IV. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 presents a normalized intensity cross-section of an Airy fielddistribution.

FIG. 2 presents changes in PSF characteristics for optical systems withcentral obscurations.

FIG. 3 presents relative changes in PSF cross-sections for opticalsystems with pupil phase masks.

FIG. 4 presents Strehl ratios for optical systems with amplitude andphase masks as a function of the masks' radial sizes.

FIGS. 5 and 6 present the near field and the far field intensitydistributions, respectively, for a diffraction-limited optical systemwith a circular-shaped uniformly illuminated pupil.

FIGS. 7 and 8 present the near field and the far field intensitydistributions, respectively, for a diffraction-limited optical systemwith a doughnut-shaped uniformly illuminated pupil.

FIG. 9 presents the near field intensity distributions for an opticalsystem containing input apertures arranged in a circular pattern.

FIGS. 10 through 12 present the far field intensity distributions of anoptical system with the near field distribution shown in FIG. 9, fordifferent wavefront distortions of the incoming field.

FIG. 13 presents the near field intensity distribution of an OPAcomprised of seven circular-shaped laser beams with Gaussian intensityprofiles.

FIGS. 14 and 15 present the far field intensity distributions of an OPAcomprised of seven circular-shaped laser beams with Gaussian intensityprofiles for different wavefront distortions of the propagating beams.

FIGS. 16 through 23 present examples of two-dimensional patternsemployed to diffract a fraction of the optical field in accordance withthe present invention.

FIG. 24 presents an optical layout of the first embodiment of thepresent invention.

FIG. 25 presents the relative power contained within the central node ofthe transformed output field as a function of the phase zone radius inaccordance with the first embodiment of the present invention.

FIG. 26 presents the two-dimensional intensity distribution of theoptical field in the back focal plane of the optical system 101 inaccordance with the first embodiment of the present invention.

FIG. 27 presents the two-dimensional phase distribution of the opticalfield in the back focal plane of the optical system 101 aftermodification by the first phase structure in accordance with the firstembodiment of the present invention.

FIGS. 28 and 29 present the respective two-dimensional intensity andphase distributions of the modified optical field in the Fraunhoferregion in accordance with the first embodiment of the present invention.

FIG. 30 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region after additional modification bythe second phase structure in accordance with the first embodiment ofthe present invention.

FIGS. 31 and 32 present the three-dimensional intensity distributions ofthe transformed optical field in accordance with the first embodiment ofthe present invention.

FIG. 33 presents axial cross-sections of the relative intensitydistributions of the transformed optical field for three aperture radiiof the output lens in accordance with the first embodiment of thepresent invention.

FIG. 34 presents the two-dimensional phase distribution of the opticalfield in the back focal plane of the optical system 101 aftermodification by the first phase structure in accordance with the firstembodiment of the present invention.

FIG. 35 presents the two-dimensional intensity distribution of thediffracted optical field in the Fraunhofer region in accordance with thefirst embodiment of the present invention.

FIG. 36 presents the two-dimensional phase distribution of thediffracted optical field in the Fraunhofer region in accordance with thefirst embodiment of the present invention.

FIG. 37 presents the two-dimensional phase distribution of thediffracted optical field in the Fraunhofer region, after modification bythe second phase structure in accordance with the first embodiment ofthe present invention.

FIG. 38 presents the two-dimensional intensity distribution of thetransformed optical field in accordance with the first embodiment of thepresent invention.

FIG. 39 presents the axial cross-sections of the intensity distributionsof the transformed optical field in the output plane 108 for threeaperture radii of the output lens in accordance with the firstembodiment of the present invention.

FIG. 40 presents an optical layout of the second embodiment of thepresent invention.

FIG. 41 presents the two-dimensional intensity distribution of theoriginal PSF produced by the optical system with central obscuration inaccordance with the second embodiment of the present invention.

FIG. 42 presents the two-dimensional phase distribution of the PSF aftermodification by the first phase structure in accordance with the secondembodiment of the present invention.

FIG. 43 presents the two-dimensional intensity distribution of themodified PSF in the Fraunhofer region in accordance with the secondembodiment of the present invention.

FIG. 44 presents the two-dimensional phase distributions of the modifiedPSF in the Fraunhofer region in accordance with the second embodiment ofthe present invention.

FIG. 45 presents the phase distribution of the modified PSF in theFraunhofer region after additional modification by the second phasestructure in accordance with the second embodiment of the presentinvention.

FIGS. 46 through 48 present three-dimensional intensity distributions ofthe transformed PSF in accordance with the second embodiment of thepresent invention

FIG. 49 presents axial cross-sections of the relative intensitydistributions of the transformed PSF for three aperture radii of theoutput lens in accordance with the second embodiment of the presentinvention.

FIG. 50 presents the two-dimensional phase distributions of the PSFafter modification by the first phase structure in accordance with thesecond embodiment of the present invention.

FIG. 51 presents the two-dimensional intensity distribution of themodified PSF in the Fraunhofer region in accordance with the secondembodiment of the present invention.

FIG. 52 presents the two-dimensional phase distribution of the modifiedPSF in the Fraunhofer region in accordance with the second embodiment ofthe present invention.

FIG. 53 presents the phase distribution of the modified PSF in theFraunhofer region after additional modification by the second phasestructure in accordance with the second embodiment of the presentinvention.

FIG. 54 presents the three-dimensional intensity distributions of thetransformed PSF in accordance with the second embodiment of the presentinvention.

FIG. 55 presents the axial intensity cross-sections of the transformedPSF for three aperture radii of the output lens in accordance with thesecond embodiment of the present invention.

FIG. 56 presents the phase pattern of the first phase structure inaccordance with the second embodiment of the present invention.

FIG. 57 presents the two-dimensional phase distribution of the PSF aftermodification by the first phase structure in accordance with the secondembodiment of the present invention.

FIG. 58 presents the two-dimensional intensity distribution of themodified PSF in the Fraunhofer region in accordance with the secondembodiment of the present invention.

FIG. 59 presents the two-dimensional phase distribution of the modifiedPSF in the Fraunhofer region in accordance with the second embodiment ofthe present invention.

FIG. 60 presents the phase distribution of the modified PSF in theFraunhofer region after additional modification by the second phasestructure in accordance with the second embodiment of the presentinvention.

FIG. 61 presents the three-dimensional intensity distributions of thetransformed output field in accordance with the second embodiment of thepresent invention.

FIG. 62 presents an optical layout of the third embodiment of thepresent invention.

FIG. 63 presents the two-dimensional intensity distribution of thefocused optical field in accordance with the third embodiment of thepresent invention.

FIG. 64 presents the two-dimensional phase distribution of the focusedoptical field after modification by the first phase structure inaccordance with the third embodiment of the present invention.

FIG. 65 presents the two-dimensional intensity distribution of themodified optical field in the Fraunhofer region in accordance with thethird embodiment of the present invention.

FIG. 66 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region in accordance with the thirdembodiment of the present invention.

FIG. 67 presents the phase distribution of the second phase structure inaccordance with the third embodiment of the present invention.

FIG. 68 presents the resulting two-dimensional phase distribution of themodified optical field in the Fraunhofer region after additionalmodifications by the second phase structure in accordance with the thirdembodiment of the present invention.

FIGS. 69 and 70 present the three-dimensional intensity distributions ofthe transformed optical field in the Fraunhofer region in accordancewith the third embodiment of the present invention.

FIG. 71 presents the relative intensity cross-sections of thetransformed output field for three aperture radii values of the outputlens in accordance with the third embodiment of the present invention.

FIG. 72 presents the two-dimensional phase distribution of the secondphase structure in accordance with the third embodiment of the presentinvention.

FIG. 73 presents the two-dimensional phase distribution of the opticalfield in the Fraunhofer region after modifications by the second phasestructure in accordance with the third embodiment of the presentinvention.

FIGS. 74 and 75 present the three-dimensional intensity distributions ofthe transformed output field in accordance with the third embodiment ofthe present invention.

FIG. 76 presents the relative intensity cross-sections of thetransformed output field for three aperture radii values of the outputlens in accordance with the third embodiment of the present invention.

FIG. 77 presents the relative intensity cross-sections of thetransformed output fields produced with the output lens employing a 50.0mm aperture radius in accordance with the third embodiment of thepresent invention.

FIG. 78 presents the two-dimensional intensity distribution of thefocused optical field in the presence of wavefront distortions at thesystem input in accordance with the third embodiment of the presentinvention.

FIG. 79 presents the two-dimensional phase distribution of the focusedoptical field in the presence of wavefront distortions at the systeminput after modification by the first phase structure in accordance withthe third embodiment of the present invention.

FIG. 80 presents the two-dimensional intensity distribution of thefocused optical field in the presence of alternative wavefrontdistortions at the system input in accordance with the third embodimentof the present invention.

FIG. 81 presents the two-dimensional phase distribution of the focusedoptical field in the presence of alternative wavefront distortions atthe system input after modification by the first phase structure inaccordance with the third embodiment of the present invention.

FIG. 82 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region in the presence of wavefrontdistortions at the system input in accordance with the third embodimentof the present invention.

FIG. 83 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region in the presence of wavefrontdistortions at the system input after additional modification with thesecond phase structure in accordance with the third embodiment of thepresent invention.

FIG. 84 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region in the presence of alternativewavefront distortions at the system input in accordance with the thirdembodiment of the present invention.

FIG. 85 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region in the presence of alternativewavefront distortions at the system input after additional modificationwith the second phase structure in accordance with the third embodimentof the present invention.

FIG. 86 presents the phase pattern of the first phase structure inaccordance with the third embodiment of the present invention.

FIG. 87 presents the two-dimensional phase distributions of the focusedoptical field after modification by the first phase structure inaccordance with the third embodiment of the present invention.

FIG. 88 presents the two-dimensional intensity distribution of theoptical field in the Fraunhofer region modified by the first phasestructure in accordance with the third embodiment of the presentinvention.

FIG. 89 presents the two-dimensional phase distribution of the opticalfield in the Fraunhofer region modified by the first phase structure inaccordance with the third embodiment of the present invention.

FIG. 90 presents the phase distribution of the optical field in theFraunhofer region after additional modification by the second phasestructure in accordance with the third embodiment of the presentinvention.

FIG. 91 presents the three-dimensional intensity distributions of thetransformed optical field in accordance with the third embodiment of thepresent invention.

FIG. 92 presents the two-dimensional intensity distribution of thefocused optical field after obstruction by the first amplitude structurein accordance with the third embodiment of the present invention.

FIG. 93 presents the two-dimensional intensity distribution of themodified optical field in the Fraunhofer region after obstruction by thefirst amplitude structure in accordance with the third embodiment of thepresent invention.

FIG. 94 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region after obstruction by the firstamplitude structure in accordance with the third embodiment of thepresent invention.

FIG. 95 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region after additional modifications bythe second phase structure in accordance with the third embodiment ofthe present invention.

FIG. 96 presents the three-dimensional intensity distribution of thetransformed optical field in accordance with the third embodiment of thepresent invention.

FIG. 97 presents the optical layout of the fourth embodiment of thepresent invention.

FIG. 98 presents the two-dimensional array of phase shifting elementslocated at the input of the optical system in accordance with the fourthembodiment of the present invention.

FIG. 99 presents the two-dimensional irradiance distribution of thefocused optical field in accordance with the fourth embodiment of thepresent invention.

FIG. 100 presents the two-dimensional phase distribution of the focusedoptical field after modification by the first phase structure inaccordance with the fourth embodiment of the present invention.

FIG. 101 presents the first phase structure located within the focusedoptical field in accordance with the fourth embodiment of the presentinvention.

FIG. 102 presents the two-dimensional intensity distribution of themodified optical field in the Fraunhofer region in accordance with thefourth embodiment of the present invention.

FIG. 103 presents the two-dimensional phase pattern of the second phasestructure in accordance with the fourth embodiment of the presentinvention.

FIG. 104 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region after additional modifications bythe second phase structure in accordance with the fourth embodiment ofthe present invention.

FIGS. 105 and 106 present the three-dimensional irradiance distributionsof the transformed optical field in accordance with the fourthembodiment of the present invention.

FIG. 107 presents the relative irradiance cross-sections of thetransformed output field for three aperture radii values of the outputlens in accordance with the fourth embodiment of the present invention.

FIG. 108 presents the optical layout of the fifth embodiment of thepresent invention.

FIG. 109 presents the two-dimensional irradiance distribution of thefocused OPA field in the presence of wavefront distortions in accordancewith the fifth embodiment of the present invention.

FIG. 110 presents the two-dimensional phase distribution of the focusedOPA field in the presence of wavefront distortions after modification bythe first phase structure in accordance with the fifth embodiment of thepresent invention.

FIG. 111 presents the two-dimensional irradiance distribution of themodified optical field in the Fraunhofer region in accordance with thefifth embodiment of the present invention.

FIG. 112 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region in accordance with the fifthembodiment of the present invention.

FIG. 113 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region after additional phasemodifications by the second phase structure in accordance with the fifthembodiment of the present invention.

FIG. 114 presents the two-dimensional irradiance distribution of thetransformed output optical field in accordance with the fifth embodimentof the present invention.

FIG. 115 presents the two-dimensional phase distribution of the modifiedoptical field in the Fraunhofer region after additional phasemodifications by the second phase structure in accordance with the fifthembodiment of the present invention.

FIG. 116 presents the two-dimensional irradiance distribution of thetransformed output optical field in accordance with the fifth embodimentof the present invention.

FIG. 117 presents the three-dimensional intensity distribution of thetransformed output field in accordance with the fifth embodiment of thepresent invention.

V. DETAILED DESCRIPTION

The present invention is further described in detail in the form ofspecific embodiments. However, the present invention is not limited toonly the specific embodiments described herein, and can be employed in abroad range of various alterations of the disclosed embodiments.

While radiation with wavelengths of 0.55 micrometers and 1.0 micrometerswere employed in the following embodiments to illustrate the operationalprincipals of the present invention, it should be clear for thoseskilled in the art that the teachings of this invention can be appliedto optical systems operating within other regions of electromagneticspectra, including the extreme ultraviolet, ultraviolet, visible,infrared, and terahertz radiation regions.

The present invention discloses the implementation details of coherentoptical field transformation techniques, and the associated opticalsystems based on a combination of several optical elements to producecontrolled coherent interactions within the output optical field. Thetechnique can be applied to modify various incoming optical fields,including PSFs of optical systems, as well as the field distributionsfrom lasers and coherent laser arrays. In accordance with the presentinvention, the incoming optical field is first transformed into a farfield distribution by an optical system. In the case of the PSFtransformations this step is not required. The transformed fielddistribution can be produced in the form of irradiance distribution at afinite distance from an optical system performing the fieldtransformation. Alternatively, the transformed field can be produced inthe form of a radiance distribution in the far field from the apertureof the optical system transforming the field.

The transforming optical system contains a diffractive structure placedwithin the coherent optical field to produce localized phase oramplitude discontinuities to the field. The field discontinuitieseffectively split the optical radiation into two fractions. The firstfraction is caused by diffraction of the field on the localizeddiscontinuities of the diffractive structure. The second fraction of thefield bypasses the localized discontinuities of the diffractivestructure, and therefore is not affected by diffraction. Thetransforming optical system also contains a lens with positive opticalpower that produces Fraunhofer diffraction region of the propagatingfield. The transforming optical system also contains a phase structureplaced in the Fraunhofer diffraction region that produces optical pathmodifications to localized regions of the optical field. The transformedoptical field is formed in the far field with respect to the phasestructure located in the Fraunhofer diffraction region. Alternatively,the transforming optical system may contain a lens with positive opticalpower that follows the phase structure and produces the transformedoptical field in its back focal plane. The coherent interactions withinthe far field are achieved by the relative adjustments in the fractionalfield powers, as well as the adjustments in OPD between the diffractedand non-diffracted fractions of the field. Both transmissive andreflective optical components and phase structures may be employed tomodify the optical field in accordance with the present invention. Insome applications, an additional phase structure can be employed as partof the transforming optical system to reduce wavefront distortionswithin the optical fields. By appropriately selecting properties of theoptical components within the transforming optical system, as well astheir relative size and placement within the system, significantflexibility in controlling the shape of the transformed output field isachieved.

The present invention can be applied to transform PSFs produced byoptical systems, such as objective lenses, telescopes, concave mirrors,etc. The invention can also be applied to transform coherent opticalfields, such as the fields produced by laser emitters and theircombinations, into OPAs.

Transformations of the optical fields in accordance with the presentinvention are performed in several steps. During the first step, farfield distributions of the incoming radiation are formed at, or in thevicinity of, a focal plane of an optical system.

During the second step, the far field distributions are modified by adiffractive structure placed within the formed far field. Thediffractive structure contains phase or amplitude patterns that diffractfractions of the optical field.

During the third step, the optical field diffracted by the structure istransformed by an optical system into a Fraunhofer diffraction pattern.This transformation can be achieved by moving away from the opticalfield to satisfy the far field criterion. Alternatively, opticalcomponents with positive power can be employed to perform thetransformation. The location of the Fraunhofer region within the opticalsystem depends on the optical power of the components and theirplacement with respect to the optical field, as will be described inmore detail in the following embodiments. Diffraction of the field bythe diffractive structure results in non-uniform intensity and phasedistributions within the Fraunhofer diffraction region.

During the fourth step, controlled optical path modifications areproduced within localized areas of the field in the Fraunhoferdiffraction region that result in coherent interactions between thefractions of the radiation at the system output. The controlled opticalpath modifications are produced by a phase structure placed within theoptical field in the Fraunhofer diffraction region. The phase structuremay also locally control the amplitude of the optical field.

During the fifth step, the optical field modified by the phase structureis transferred from the Fraunhofer diffraction region to the far fieldconjugate location, where coherent interactions between the differentfractions of the optical field are produced. This transfer is achievedby propagating the modified optical field to the back focal plane of alens with positive optical power, or by propagating the modified opticalfield over a significant distance from the system aperture to satisfythe far field condition, as will be described in more detail in thefollowing embodiments.

Combinations of the OPDs produced by the first and second structures, aswell as the localized size and shape of their respective patterns, offera significant flexibility in transforming the optical fields and resultin a variety of transformed output fields with different shapes andsizes.

Additional modifications to the transformed field can be produced byadjusting the lateral size of the field within the Fraunhoferdiffraction region with changes to the f-number or aperture size withinthe transforming optical system. The f-number can be adjusted bychanging the optical power of components within the system, or bychanging the aperture size of the optical components within the system.

In accordance with the present invention, the relative size and shape ofthe diffractive structure pattern is selected to modify the size andshape of the transformed output field and to redistribute the fractionalfield power within the transformed output field. For example, therelative size and shape of the phase pattern of the diffractivestructure can be employed to adjust the size and shape of thetransformed field.

FIGS. 16 through 23 show examples of the phase pattern contained in thediffractive structure. The phase patterns constitute localized phasesteps that introduce OPDs to the wavefront of the propagating radiation,and are shown in FIGS. 16 through 23 with a darker color. In thesimplest case, the phase steps of the first phase structure may besquare or circular in shape, as shown in FIGS. 16 and 17, respectively.The phase steps may also take a variety of alternative shapes and sizes,including a rectangular-shaped pattern shown in FIG. 18, adoughnut-shaped pattern shown in FIG. 19, multiple phase steps shown inFIG. 20, and a hollow rectangular-shaped pattern shown in FIG. 21. Thephase steps may also have a variety of gradual phase transitions, asshown in FIG. 22 for a Gaussian-shaped phase step, and in FIG. 23 for acircular phase step having an apodized edge with gradually changingphase. More complex patterns of the first phase structure can beproduced, for example, as various combinations of the phase primitivesshown in FIGS. 16 through 23.

In the absence of wavefront distortions of the focused optical field,efficient field transformation can be achieved when the OPDs produced bythe first phase structures are the product of an odd integer j and halfof the radiation wavelength 0.5λ, as defined by equation (2). In someapplications, the lowest value of OPD=0.5.1, corresponding to the lowestodd integer j=1, is employed. In the presence of wavefront distortions,or when the local shape of the transformed field needs to be altered,the OPDs produced by the phase patterns may no longer be equal to thevalues defined by the equation (2), as will be further shown in thefollowing embodiments.

The disclosed technique for the coherent transformation of optical fielddistributions may also include a means for adjusting the size and shapeof the resulting output fields. In accordance with the presentinvention, adjustments in the lateral size and shape of the transformedfields are performed using electronically controlled devices such asspatial light modulators (SLMs). SLMs may be employed to dynamicallyadjust the lateral size and shape of the phase structures, thereforealtering the resulting size and shape of the transformed output fields.Examples of SLMs suitable for controlling the transformed fielddistributions in accordance with the present invention may include, butare not limited to: liquid crystal on silicone (LCOS) SLMs manufacturedby Boulder Nonlinear Systems, translucent Liquid Crystal Display (LCD)and reflective (LCOS) SLMs manufactured by HOLOEYE Photonics AG, andDigital Micromirror Devices (DMDs) manufactured by Texas Instruments,Inc.

The peak value, shape, and size of the transformed field distributionsin accordance with the present invention are defined by the specificproperties and location of the optical components comprising the opticalsystem that transforms the optical field. Details of the disclosedtechniques for transforming focused field distributions, as well as theoptical devices for their implementation, will be explained in detail inthe following embodiments.

First Embodiment

The first embodiment of the present invention is designed to transformPSF distributions of diffraction-limited optical systems with uniformlyilluminated circular apertures, also known as Airy distributions. FIG.24 shows the optical layout corresponding to the first embodiment of thepresent invention. It shows a diffraction-limited optical system 101producing an Airy distribution in its back focal plane, as well as anoptical system 102 for transforming the Airy distribution. The inputintensity distribution and the Airy intensity distribution in the focalplane of a diffraction-limited optical system were shown earlier inFIGS. 5 and 6, respectively.

The optical system 102 in accordance with the first embodiment of thepresent invention transforms the PSF distribution of thediffraction-limited optical system 101 and produces the transformedoptical field in the output plane 108. The optical system 102 contains adiffractive structure 103 placed within the focused optical field in theback focal plane of the optical system 101, a lens 104 with positiveoptical power located in proximity to the first diffractive structure103, a lens 105 with positive optical power located at the front focaldistance from the lens 104, a phase structure 106 located after the lens105, and a lens 107 with positive optical power located after the phasestructure 106. To reduce the axial distance of the optical layout, theoptical components 105, 106, and 107 are placed in proximity to eachother. The output plane 108 is located in the back focal plane of thelens 107.

An optional phase structure, not shown in FIG. 24, may also be insertedinto the optical path of the optical system 101 to compensate forwavefront distortions of the incoming optical field. When the incomingoptical field is not distorted, the incoming radiation propagatesthrough the diffraction-limited optical system 101 and forms an Airydistribution at the back focal plane of the optical system 101. Thestructure 103 is placed at the back focal plane of the optical system101 and diffracts a fraction of the focused Airy distribution byintroducing localized OPDs to the focused optical field. In accordancewith the first embodiment, the diffractive structure 103 contains aphase step. The phase step size of the diffractive phase structure 103is selected to be less than the size of the central node of the Airydistribution. The diffracted field further propagates through the lenselement 104, placed in proximity to the diffractive phase structure 103,onto the lens element 105 placed in the back focal plane of the lenselement 104. The focal lengths of the lens elements 104 and 105 areequal to each other. The lens element 105 collimates the field modifiedby the elements 103 and 104, and directs it onto the phase structure106. The phase structure 106 is located in the back focal plane of thelens element 104, corresponding to the Fraunhofer diffraction region ofthe radiation diffracted by the phase structure 103.

The phase structure 106 modifies the field by producing localized OPDswithin the Fraunhofer diffraction region. The size of the phasestructure 106 is selected to affect only a fraction of the field in theFraunhofer diffraction region. By adjusting the OPDs produced by thephase structure 106 within the Fraunhofer diffraction region, shapemodifications of the transformed field within the output plane 108 areproduced.

The field modified by the phase structure 106 propagates through thefocusing lens 107, and forms the transformed PSF distribution in theoutput plane 108. The axial distance between the optical components 106and 107 can be adjusted based on the packaging requirements of thesystem. The output plane 108 is located in the back focal plane of thelens 107. The axial location of the observation plane 108 can bemodified by changing the focal length of the lens element 107. Thelateral size of the transformed field produced in the output plane 108is proportional to the magnification of the optical system 102 and thesize of the phase pattern of the diffractive structure 103. Therefore,the lateral size of the transformed field in the output plane 108 can beadjusted by changing the focal lengths of the lenses 104, 105, and 107or the phase pattern size of the diffractive structure 103. The focallengths of the lens elements 104, 105, and 107, in accordance with thefirst embodiment of the present invention, are equal, and therefore theoptical system 102 has a magnification of M=−1. When the structures 103and 106 are absent from the system 102, the system will produce in theoutput plane 108 an image conjugate of the PSF from thediffraction-limited optical system 101.

Although the diffractive structure 103 and the lens 104 with positiveoptical power are shown in FIG. 24 as two optical elements located inproximity to each other, they can be combined into a single opticalelement that performs both functions of the two elements. In that case,one of the element's surfaces will contain the features of thediffractive phase structure 103, while the other surface of the elementwill produce the optical power of the lens 104. In a similar way, thesecond phase structure 106 can be combined with either of the lenses 105or 107 to form a single optical element. One of the element's surfaceswill contain the phase structure, while the other surface of the elementwill produce the optical power of the respective lens.

The lens elements 105 and 107 can also be combined into a single lenswith optical power equal to the sum of the optical powers of the lenses105 and 107. In the most general case, the phase structure 106 and thelens elements 105 and 107 can be combined into a single optical elementthat performs the functions of the phase structure and the lenselements. The phase profile of the phase structure 106 can be fabricatedon one of the element surfaces, or embedded into the element.

In accordance with the first embodiment of the present invention, theoptical system 101 has an aperture diameter of d₁₀₁=8 mm and a focallength of f₁₀₁=500 mm. The wavelength of the propagating radiation is 1micron, which, in accordance with equation (1), results in an Airy diskdiameter of 0.1525 mm.

The diffractive structure 103 and the phase structure 106 containcircular-shaped phase steps, similar to the phase step shown in FIG. 17.The phase steps of the structures 103 and 106 are centered with respectto the propagating field and introduce an optical path differenceOPD=j0.5λ in accordance with equation (2) to the localized fractions ofthe propagating radiation, where j is an odd integer. When the phasestructures 103 and 106 are fabricated as phase relief profiles onto therespective substrates, the height of the phase steps h is calculated as:

h=OPD/(n−1)  (3)

where n is the refractive index of the phase structure substratematerial. For the phase structures 103 and 106 substrates made of BK7glass with a refractive index n=1.5075 corresponding to a wavelength λ=1micron of the propagating radiation and j=1, the step height h of thephase structures corresponding to OPD=0.5λ is equal to 0.9852 microns.

The focal lengths of the lenses 104, 105, and 107 are f₁₀₄=f₁₀₅=f₁₀₇=100mm, and the axial distances between the phase structures 103 and 106, aswell as between the phase structure 106 and the output plane 108, arealso equal to 100 mm.

The diffractive structure 103 contains a single phase step with theradius r₁. The phase structure 106 also contains a single phase stepwith the radius r₂=0.8 mm defined by the following equation:

r ₂=(d ₁₀₁ f ₁₀₄)/(2f ₁₀₁)  (4)

For a given phase step radius r₂ of the phase structure 106, the shapeof the modified field distribution produced at the output plane 108depends on the phase step radius r₁ of the diffractive structure 103.The relative radiation power contained within the central node of themodified field distribution at the output plane 108 also depends on thephase step radial size r₁ of the diffractive structure 103, and is shownin FIG. 25. The radial size r₃ of the central node of the modified fielddistribution at the output plane 108 in accordance with the firstembodiment of the present invention is equal to the radial phase stepsize r₁ of the diffractive structure r₃=r₁.

The shape of the modified field distribution produced at the outputplane 108 also depends on the f-number of the system defined by thesmallest aperture size of the two lenses 105 and 107. When the aperturesof the lenses 105 and 107 are large, corresponding to small f-numbers,diffraction effects and field truncations on the lens apertures do notalter the shape of the transformed field within the output plane 108.With a reduction in the lens aperture sizes and the respective increasein the f-number of the optical system 102, diffraction effects startplaying an important role in shaping the transformed field in the outputplane 108.

When the phase step radius r₁ of the diffractive structure 103 isadjusted to r₁=22 microns, the transformed field distribution in theoutput plane 108 will contain the maximum power of the propagatingradiation within the central node, as shown in FIG. 25. FIG. 26 presentsa two-dimensional intensity distribution of the focused optical fieldproduced by the optical system 101 in the back focal plane in accordancewith the first embodiment of the present invention. FIG. 27 presents atwo-dimensional phase distribution of the focused optical field in theback focal plane of the optical system 101 after modification by thediffractive phase structure 103 containing a circular phase step withradius of r₁=22 microns.

FIGS. 28 and 29 present the respective two-dimensional intensity andphase distributions of the modified optical field in the Fraunhoferdiffraction region after the lens element 105 and prior to entering thephase structure 106. The two-dimensional field distributions in in theFraunhofer diffraction region are non-uniform with respect to bothintensity and phase. FIG. 30 presents the two-dimensional phasedistribution of the modified optical field in the Fraunhofer regionafter modification produced by the second phase structure 106. FIG. 30shows the addition of an OPD by the circular phase step of the phasestructure 106 with a radial size of r₂=0.8 mm. The OPD produced by thephase structure 106 enhances the fractional power contained in thecentral node of the transformed field in the output plane by reducingthe phase discontinuities between the phase step and the phase regionsurrounding the step, as shown in FIG. 30. FIGS. 31 and 32 present thethree-dimensional intensity distributions of the transformed opticalfields at the output plane 108 corresponding to the respective radialsizes of the lens 107 aperture of 100 mm and 10 mm. FIG. 33 presents theaxial cross-sections of the relative intensity distributions of thetransformed optical fields at the output plane 108 for three differentaperture radii of the output lens 107. The three output fielddistributions shown in FIG. 33 correspond to the radial aperture sizesof 100 mm, 15.5 mm, and 3.9 mm, and contain within the 22 micronscentral peak radius of the transformed output field 99.4%, 95.8%, and82.3% of the propagating radiation power, respectively.

Adjustments to the radius r₁ of the diffractive phase structure 103alter the fractional power contained within the central node of thetransformed field, as shown in FIG. 25. When the radius r₁ of thediffractive phase structure 103 is adjusted to r₁=48 microns, thetransformed field in the output plane 108 will contain a minimumradiation power in the center. FIGS. 34 through 39 present fielddistributions of the first embodiment, when the radius r₁ of the phasestructure 103 was adjusted to r₁=48 microns. FIG. 34 presents thetwo-dimensional phase distribution of the optical field in the backfocal plane of the optical system 101 after modification by thediffractive structure 103. The phase distribution in FIG. 34 containsthe OPD produced by the circular phase step of the diffractive structure103 with the radius of r₁=48 microns. FIGS. 35 and 36 present therespective two-dimensional intensity and phase distributions of thediffracted optical field in the Fraunhofer region prior to the phasestructure 106. FIGS. 35 and 36 reflect the fact that the optical fieldin the Fraunhofer diffraction region is non-uniform with respect to bothintensity and phase. FIG. 37 presents the two-dimensional phasedistribution of the optical field in the Fraunhofer diffraction regionafter the OPD produced by the phase structure 106. It contains OPDproduced by the circular phase step of the phase structure 106 with aradial size of r₂=0.8 mm. The OPD produced by the phase structure 106results in increased phase discontinuities within the Fraunhoferdiffraction field, as shown in FIG. 37. FIG. 38 presents thetwo-dimensional intensity distribution of the transformed optical fieldin the output plane 108 corresponding to a 50 mm radial size of the lens107 aperture. FIG. 39 presents the axial cross-sections of the relativeintensity distributions of the transformed optical fields in the outputplane 108 with suppressed central node peaks for three different radialapertures of the lens 107. The axial cross-sections shown in FIG. 39correspond to the lens 107 radial aperture values of 50 mm, 5.5 mm, and2.0 mm and contain within the axial region with a radial size of 48microns 0.1%, 4.1%, and 7.5% of the transformed output field power,respectively.

Second Embodiment

The second embodiment of the present invention is designed to transformPSF distributions of optical systems with central obscurations. Thistype of optical system is commonly found in reflective astronomicaltelescopes. The optical layout of the second embodiment of the presentinvention is presented in FIG. 40. It shows the optical system 200 withcentral obscuration producing a PSF distribution in the back focalplane, as well as the optical system 203 for transforming the PSF of theoptical system 200 and producing the transformed optical fielddistribution in the output plane 206. The optical system 200 consists ofa primary mirror 201 with a central opening and a secondary mirror 202obstructing the aperture of the primary mirror 201. The uniformlyilluminated aperture and the PSF intensity distribution of an opticalsystem with central obscuration were shown in FIGS. 7 and 8,respectively.

In accordance with the second embodiment, the primary mirror 201 of theoptical system 200 has an aperture diameter d₂₀₁=8 mm, and the secondarymirror 202 of the optical system 200 obscures the aperture of theprimary mirror 201 and has a diameter d₂₀₂=5 mm. The effective focallength f₂₀₀ of the optical system 200 with central obscuration isf₂₀₀=500 mm. When the wavelength of the radiation is 1 micron, the PSFcentral core diameter produced by the optical system 200 in the backfocal plane is approximately 116 microns.

The optical system 203 in accordance with the second embodiment of thepresent invention contains two optical elements 204 and 205 withpositive optical power, and produces the transformed field distributionsin the output plane 206. The optical element 204 is placed at the backfocal plane of the optical system 200, and the element 205 is located inthe back focal plane of the element 204. The modified fielddistributions are produced in the output plane 206 located after theelement 205 at the image conjugate location with respect to the backfocal plane of the optical system 200. The axial distance L₁ between theback focal plane of the optical system 200 and the element 205 is oftenselected to be equal to the focal length f₂₀₄ of the lens element 204,i.e. L₁=f₂₀₄. The distance L₂ between the optical element 205 and theoutput plane 206 is a function of the focal lengths f₂₀₄ and f₂₀₅ of therespective optical elements 204 and 205 contained within the opticalsystem 203, and is defined as:

$\begin{matrix}{L_{2} = \frac{f_{204}f_{205}}{f_{204} - f_{205}}} & (5)\end{matrix}$

When the focal length of the element 204 is twice the focal length ofthe element 205, i.e. when f₂₀₄=2f₂₀₅, the two axial distances L₁ and L₁are equal to each other L₁=L₂=2f₂₀₅. It should be noted that inaccordance with the second embodiment, the focal length f₂₀₅ of theelement 205 cannot exceed the focal length f₂₀₄ of the element 204.

The element 204 of the optical system 203 contains a diffractive phasestructure 207 fabricated on one of the element's surfaces. While theshape of the lens surface containing the phase structure 207 can beconvex, planar, or concave, in accordance with the second embodiment,the surface containing the phase structure 207 was selected to beplanar. The surface 208 is convex-shaped to produce positive opticalpower to the element 204. The element 205 of the optical system 203contains a second phase structure 209 fabricated on one of the element'ssurfaces. The shape of the element's surface containing the phasestructure 209 can be convex, planar, or concave, and was selected to beplanar in accordance with the second embodiment. The lens surface 210 isconvex-shaped to produce positive optical power to the element. Thefractional radiation power contained within the central node of thetransformed field in the output plane 206 depends on the lateral sizeand shape of the phase steps of the phase structures 207 and 209. Anoptional third phase structure, not shown in FIG. 40, can be insertedinto the optical path prior to the optical system 200, or after thefirst element 204, to compensate for wavefront distortions in theoptical field.

The incoming radiation propagates through the diffraction-limitedoptical system 200 with central obscuration and forms a PSF fielddistribution at the output of said optical system 200. When the objectis located at infinity, the PSF is formed in the back focal plane of theoptical system 200. The optical system 203 transforms the PSF andproduces the transformed optical field at the output plane 206. Thefirst element 204 of the optical system 203 containing the diffractivestructure 207 is placed after the optical system 200 so that thediffractive structure 207 is co-located with the PSF distribution of theoptical system 200. The structure 207 diffracts a fraction of the PSFfield by introducing localized phase discontinuities to the opticalfield.

Both diffracted and non-diffracted fractions of the PSF are furthermodified by the lens surface 208 of the lens element 204 and aredirected onto the surface of the element 205 containing the phasestructure 209. The phase structure 209 is positioned within theFraunhofer diffraction pattern of the radiation diffracted by the phasestructure 207. In accordance with the second embodiment, the phasestructure 209 is placed in the back focal plane of the element 204. Thephase structure 209 contained within the element 205 modifies theoptical field within the Fraunhofer region by introducing localized OPDsto fractions of the field. The optical field is further modified by theconvex surface 210 of the lens element 205, and is directed onto theoutput plane 206 where the transformed field distribution is produced.

The phase step of the difractive structure 207 is square-shaped, asshown in FIG. 16, and has a lateral size of h=60 microns. Thesquare-shaped step of the diffractive structure 207 produces an opticalpath difference of OPD=0.5λ to a fraction of the optical field withinthe PSF. The square-shaped phase step of the first phase structure 207is centered with respect to the PSF field in the back focal plane of theoptical system 200 and is selected to be smaller than the size of thecentral node of the PSF. The phase step is fabricated onto the planarsurface of the lens 204. When the phase structure 207 is formed as aphase relief pattern onto the surface of the lens element 204, theheight of the phase mask steps h is calculated based on equation (3).For the lens 204 made of BK7 glass with a refractive index n=1.5075 atthe working wavelength of λ=1 micron, the step height h of the phasestructure 207 corresponding to OPD=0.5λ is equal to 0.9852 microns.

The size of the phase structure 209 is selected to alter only a fractionof the field produced within the Fraunhofer diffraction region after theelement 204. By adjusting the OPD produced by the phase structure 209within the Fraunhofer diffraction region, constructive or destructiveinterference between the fractions of the propagating field within theoutput plane 206 is produced. The phase step of the phase structure 209is doughnut-shaped, as shown in FIG. 19. The doughnut-shaped phase stepintroduces a localized optical path difference of OPD=0.5λ. Thedoughnut-shaped phase step of the phase structure 209 is fabricated ontothe planar surface of the element 205 and is centered with respect tothe propagating field. The outer r_(o) and inner r_(i) radii of thedoughnut-shaped phase step of the second phase structure 209 are foundusing the following equations: r_(o)=(d₂₀₁f₂₀₄)/(2f₂₀₀) andr_(i)=(d₂₀₂f₂₀₄). In accordance with the second embodiment, the focallength of the element 204 is f₂₀₄=100 mm and the focal length of thelens 205 is f₂₀₅=50 mm. The axial distances between the elements 204 and205, and between the element 205 and the output plane 206, are bothequal to 100 mm.

The outer and inner radii of the doughnut-shaped phase step of the phasestructure 209 are calculated to be r_(o)=0.8 mm and r_(i)=0.5 mm,respectively. When the phase structure 209 is fabricated as a phaserelief pattern onto the surface of the lens element 205, the height ofthe phase mask steps h is calculated based on equation (3). For the lens205 made of BK7 glass with a refractive index n=1.5075 at the workingwavelength of λ=1 micron, the step height h of the phase structure 209corresponding to OPD=0.52 is equal to 0.9852 microns.

The transformed field central node lateral size l_(tr) produced in theobservation plane 206 is proportional to the linear size l₁ of the phasestep of the diffractive structure 207. The lateral size of thetransformed field central node intensity l_(tr) also depends on thefocal lengths f₂₀₄ and f₂₀₅ of the respective elements 204 and 205:

$\begin{matrix}{l_{tr} = \frac{l_{1}f_{205}}{f_{204} - f_{205}}} & (6)\end{matrix}$

The central node size l_(t), of the transformed field in the outputplane 206 can be adjusted based on the appropriate selection of thefocal lengths f₂₀₄ and f₂₀₅ of the respective elements 204 and 205 ofthe optical system 203. When the axial distance L₁ is twice the focallength of the lens element 205, i.e. L₁=f₂₀₄=2f₂₀₅, the central nodesize l_(t), of the transformed field in the output plane 206 is equal tothe step size of the phase structure 207 l_(tr)=l₁.

FIG. 41 presents the two-dimensional intensity distribution of the PSFproduced by the optical system 200. FIG. 42 presents the two-dimensionalphase distribution of the field produced in the back focal plane of theoptical system 200 after modification by the first phase structure 207.The phase distribution in FIG. 42 is modified by the square-shaped phasestep of the phase structure 207 producing localized optical pathdifference of OPD=0.5λ. FIG. 43 presents the two-dimensional intensitydistribution of the optical field produced in the Fraunhofer diffractionregion after the element 204. FIG. 44 presents the two-dimensional phasedistribution of the optical field produced in the Fraunhofer regionafter the element 204 and prior to modifications by the element 205containing the second phase structure 209. FIGS. 43 and 44 indicate thatboth the intensity and the phase distributions of the field produced inthe Fraunhofer diffraction region are non-uniform.

FIG. 45 presents the phase distribution of the optical field in theFraunhofer region after modification by the second phase structure 209containing a doughnut-shaped phase step. The doughnut-shaped phase stepof the second phase structure 209 introduces a localized optical pathdifference of OPD=0.5λ. The OPD produced by the doughnut-shaped phasestep of the second phase structure 209 reduces phase discontinuitieswithin the Fraunhofer diffraction region without affecting the fieldamplitude, as shown in FIG. 45.

Three-dimensional intensity distributions of the transformed fieldsproduced in the output plane 206 are shown in FIGS. 46 through 48. Thefield distributions correspond to the element 205 aperture radii of 20.0mm, 5.25 mm, and 2.75 mm, respectively. FIG. 49 shows the relativeintensity cross-sections of the transformed field distributions producedin the output plane 206 for the three element 205 aperture radii of 20.0mm, 5.25 mm, and 2.75 mm. The three transformed output fielddistributions shown in FIGS. 46 through 48 contain respectively 99%,94%, and 87% of the propagating radiation power within the square-shapedcentral node of the transformed field in the output plane 206.

Alternative shapes of the output transformed field can be achieved bychanging the size and shape of the phase pattern of the first phasestructure 207. For example, replacing the square-shaped phase step ofthe phase structure 207 with a doughnut-shaped phase step, similar tothe phase step shown in FIG. 19, while retaining the shape of the secondphase structure 209 will result in a transformed output field with asuppressed central core peak containing very limited optical radiationon-axis. In accordance with the second embodiment, the phase structure207 is made in the form of a doughnut-shaped step that is centered withrespect to the PSF field in the back focal plane of the optical system200 and introduces an optical path difference of OPD=0.5λ to a fractionof the focused optical field. The doughnut-shaped phase step of thephase structure 207 is fabricated onto the planar surface of the lens204 and has an outer radius r_(o)=60 microns and an inner radiusr_(i)=18 microns. When the phase structure 207 is produced as a phaserelief pattern onto the surface of the lens 204, the height of the phasemask step h is calculated based on equation (3). For the lens 204 madeof BK7 glass with a refractive index n=1.5075 at the wavelength of λ=1micron, the step height h of the phase structure 207 corresponding toOPD=0.5λ is equal to 0.9852 microns.

FIG. 50 presents the two-dimensional phase distributions of the PSFoptical field after modification by the diffractive structure 207containing the doughnut-shaped phase step. FIG. 51 presents thetwo-dimensional intensity distribution of the optical field in theFraunhofer diffraction region after the first element 204 and prior toentering the phase structure 209 of the second lens 205. FIG. 52 showsthe two-dimensional phase distribution of the optical field in theFraunhofer region prior to entering the phase structure 209 of thesecond lens 205. The optical field in the Fraunhofer diffraction regionis non-uniform with respect to intensity and phase, as shown in FIGS. 51and 52. FIG. 53 shows the phase distribution of the optical field in theFraunhofer diffraction region after modification by the phase structure209 of the second lens element 205. The OPD produced by thedoughnut-shaped phase step of the second phase structure 209 producesdestructive interferometric interactions between the fractions of theradiation in the output plane by reducing the phase discontinuitiesbetween the phase step and the phase regions surrounding the step. FIG.54 shows the resulting three-dimensional intensity distribution of thetransformed output field produced in the output plane 206 with thesecond lens element 205 having an aperture radius of 4.0 mm. FIG. 55presents the axial intensity cross-sections of the transformed fieldproduced in the output plane 206 with the element 205 having apertureradii of 40.0 mm, 4.0 mm, and 2.4 mm. The encircled power containedwithin the 36 microns aperture centered with respect to the radiationpattern and corresponding to the three radii shown in FIG. 55 is 0.4%,3.9%, and 3.6%, respectively.

A variety of complex shapes of the transformed output field can beproduced by employing a diffractive structure 207 containing multiplephase regions. FIGS. 56 through 61 show the formation of a complexoutput field within the output plane 206 in the presence of multiplephase regions contained within the diffractive structure 207. FIG. 56presents a phase pattern of the diffractive structure 207 composed ofthree phase regions. Two of the phase regions in FIG. 56 arecircular-shaped apodized patterns, similar to the pattern shown in FIG.23. The two apodized patterns have a radial size of 25 microns and aphase transition zone width of 20 microns. The optical path differencein the central regions of the apodized patterns with a radius of 5microns is OPD=0.5λ. The optical path difference gradually decreases toOPD=0 over the transition zone width of 20 microns. The phase pattern ofthe first phase structure 207 shown in FIG. 17a also contains arectangular central region with a length of 112 microns and a width of12 microns. The rectangular central region of the phase pattern producesan optical path difference of OPD=0.3λ to the propagating field. FIG. 57presents the two-dimensional phase distributions of the optical fieldafter modification by the diffractive structure 207 placed into thefocused field produced by the optical system 200. FIG. 57 shows that thephase pattern of the diffractive structure 207 is contained within thecentral node of the PSF. FIG. 58 presents the two-dimensional intensitydistribution of the modified optical field in the Fraunhofer diffractionregion prior to entering the planar surface of the element 205containing the second phase structure 209. FIG. 59 shows thetwo-dimensional phase distributions of the modified optical field in theFraunhofer region prior to entering the planar surface of the element205 containing the second phase structure 209. FIGS. 58 and 59 indicatethat the Fraunhofer diffraction field is non-uniform with respect toboth intensity and phase. FIG. 60 presents the phase distribution of theoptical field in the Fraunhofer region after modification by the secondphase structure 209 containing a doughnut-shaped phase step. Thedoughnut-shaped step of the phase structure 209 introduces a localizedoptical path difference of OPD=0.25λ to the propagating radiation and iscentered with respect to the propagating field. The outer and innerradii of the doughnut-shaped phase step of the second phase structure209 are 0.8 mm and 0.5 mm, respectively. The OPD produced by thedoughnut-shaped phase step of the second phase structure 209 is designedto produce controlled interferometric interactions between the fractionsof the radiation in the output plane in accordance with the designintent by reducing the phase discontinuities between the phase step andthe phase regions surrounding the step, as shown in FIG. 60. FIG. 61shows the three-dimensional intensity distributions of the transformedoutput field produced in the output plane 206 in accordance with thesecond embodiment of the present invention, and corresponding to thesecond element 205 radial aperture of 80.0 mm.

Third Embodiment

The third embodiment of the present invention is designed to transformoptical field distributions produced by optical systems containingmultiple spatially distributed apertures. The optical layout of thethird embodiment is presented schematically in FIG. 62. The opticallayout contains an optical system 300 composed of a segmented primarymirror and a secondary mirror 307. The primary mirror of the opticalsystem 300 is comprised of six off-axis segments 301 through 306.Radiation collected by the segments 301 through 306 is reflected ontothe secondary mirror 307 and is then redirected by the secondary mirroronto an image plane, where the PSF is produced. The image plane locationdepends on the location of an object or light source with respect to theoptical system 300. For the purpose of the following discussion, weassume that objects are located at infinity, and therefore the imageplane is located in the back focal plane of the optical system 300.

The optical layout in FIG. 62 also shows an optical system 310 employedto transform the PSF distributions of the optical system 300. Theoptical system 310 contains four optical components: a diffractivestructure 311 located at the back focal plane of the optical system 300,a lens 312 with positive optical power located along the propagationdirection at a front focal distance from the diffractive structure 311,a phase structure 313 located along the propagation direction in theback focal plane of the lens 312, and a lens 314 with positive opticalpower located along the propagation direction after the phase structure313. The lens components 312 and 314 jointly form an optical system thatre-images the focal plane of the optical system 300 onto the outputplane 315.

The axial distance between the phase structure 313 and the lens 314 canbe adjusted based on the packaging considerations for a desiredapplication. To keep the system's layout compact, the optical components313 and 314 are placed in proximity to each other. The transformed fieldis produced in the output plane 315 coinciding with the back focal planeof the lens 314. An optional third phase structure, not shown in FIG.62, can be placed into the optical path prior to the optical system 300to compensate for the wavefront distortions of the incoming radiation.Although the optical components 311 through 314 are shown in FIG. 62 astransmissive, the optical system 310 may also contain reflective phasemodulating components and mirrors.

The incoming radiation propagates through the diffraction-limitedoptical system 300 with distributed apertures and forms an image in theback focal plane. An image of a point source will produce a PSFdistribution in the back focal plane of the optical system 300. Thediffractive structure 311 of the optical system 310 is placed in theback focal plane of the optical system 300. The structure 311 diffractsa fraction of the PSF field by introducing localized phasediscontinuities to the field in the back focal plane of the opticalsystem 300. The diffracted and non-diffracted fractions of the opticalfield further propagate through the lens element 312 with positiveoptical power located at the front focal distance from the diffractivestructure 311. The lens element 312 modifies the wavefront curvature ofthe optical field and produces a Fraunhofer diffraction pattern of theoptical field modified by the diffractive structure 311. The phasestructure 313 is placed within the Fraunhofer diffraction region afterthe lens element 312. The phase structure 313 further modifies theFraunhofer diffraction pattern by introducing controlled optical pathdifferences to the fractions of the optical field. The axial distancebetween the lens element 312 and the phase structure 313 can be adjustedbased on the packaging considerations. In the case of an optical system310 employing reflective phase structures, the axial distance betweenthe lens element 312 and the phase structure 313 needs to be long enoughto prevent obstruction of the reflected field by the lens element 312.

In accordance with the third embodiment, the phase structure 313 isplaced in the back focal plane of the lens 312. In alternativeimplementations, this axial distance between the lens 312 and the phasestructure 313 can be chosen differently. In applications requiring themost compact implementation, the phase structure 313 can be placed inproximity to the lens element 312, although this selection may causesome reduction in the fractional power contained within the central nodeof the transformed output field.

The optical field modified by the phase structure 313 propagates throughthe lens 314 with positive optical power, located after the phasestructure 313. The axial distance between the phase structure 313 andthe lens element 314 can be adjusted based on the packagingconsiderations. In applications requiring the most compactimplementation, the lens element 314 can be placed in proximity to thephase structure 313. The lens 314 modifies the field curvature andtransfers the modified Fraunhofer diffraction pattern to the far fielddistribution in the back focal plane 315. The controlled optical pathmodifications by the phase structure 313 in the Fraunhofer diffractionregion produce coherent interactions of the field in the output plane315 and result in PSF shape transformations.

The primary mirror aperture of the optical system 300, in accordancewith the third embodiment, is comprised of six input apertures definedby the concave mirror segments 301 through 306, where each segmentaperture is 30 mm in diameter. The six mirror apertures are uniformlyspaced in the azimuthal direction, with the centers of the apertureslocated on the circumference of a circle with a radius of 50 mm. The sixconcave mirror segments 301 through 306 comprise a larger concaveaspheric mirror with a radius of 1484.4 mm and a conic constant of−0.63877. The secondary convex mirror is spherical with a radius of2654.9 mm. The primary and secondary mirror vertices are spaced 400 mmapart, and the back focal plane of the system is located along theoptical axis 461 mm from the vertex of the secondary mirror. Theeffective focal length of the optical system 300 with distributedapertures is f_(Eff)=1000 mm.

When the wavefront of the optical field has no distortions and theradiation reflected from all six mirrors 301 through 306 is in-phase,the resulting PSF intensity distribution in the back focal plane of theoptical system 300 has the shape shown in FIG. 63. For the propagatingradiation with a wavelength of 1 micron, the central node radius of thePSF in the back focal plane of the optical system 300 is approximately7.5 microns.

The optical system 310 is placed following the optical system 300 inorder to transform the PSF field distributions produced by the opticalsystem 300. The lenses 312 and 314 contained within the optical system310 have focal lengths of f₁=f₂=100 mm. The diffractive structure 311 isplaced in the back focal plane of the optical system 300, and contains acircular-shaped phase discontinuity with a radius of 7.3 microns. Thediffractive structure 311 is centered with respect to the optical fieldin the back focal plane of the optical system 300. The circular-shapedphase step of the structure 311 diffracts a fraction of the PSF fieldproduced in the back focal plane of the optical system 300 byintroducing a localized optical path difference of OPD=0.5λ. When thediffractive phase structure 311 is fabricated in the form of a phaserelief pattern, the height of the phase steps h within the substrate ofthe diffractive phase structure 311 is calculated based on equation (3).For the phase structure 311 made of BK7 glass with a refractive index ofn=1.5075 at the wavelength of λ=1 micron, the step height hcorresponding to an OPD=0.5λ will be 0.9852 microns. FIG. 64 shows thephase distribution of the optical field in the back focal plane of theoptical system 300 after modification by the diffractive phase structure311.

FIGS. 65 and 66 present the respective intensity and phase distributionsof the optical field modified by the diffractive structure 311 in theFraunhofer diffraction region after propagation through the lens 312.FIGS. 65 and 66 indicate that both the intensity and phase distributionsof the optical field in the Fraunhofer diffraction region are spatiallynon-uniform. The phase structure 313 contains six circular-shaped phasediscontinuities arranged in a pattern shown in FIG. 67. The phasediscontinuities of the phase structure 313 introduce localized opticalpath differences of OPD=0.5λ to the fractions of the radiation in theFraunhofer region. The phase discontinuities of the phase structure 313are oriented in the azimuthal direction to coincide with the hexagonalphase pattern of the field in the Fraunhofer region shown in FIG. 66.The radii of the phase discontinuities shown in FIG. 67, as well astheir radial distances from the optical axis, match the size and shapeof the phase pattern shown in FIG. 66. The phase discontinuities of thephase structure 313, in accordance with the third embodiment, haveaperture centers uniformly spaced along the circumference of a circlewith a radius of 5 mm, and have the radii of the individual phasediscontinuities equal to 1.5 mm. For the propagating radiation with awavelength of λ=1.0 micron and the phase relief structure 313 made froma BK7 glass substrate, the heights h of the pattern phase relief stepsfabricated onto the phase structure 313 are equal to h=0.9852 microns.

FIG. 68 shows the resulting phase distribution in the Fraunhoferdiffraction region after modification by the phase structure 313containing the phase pattern shown in FIG. 67. The optical pathdifferences produced by the phase structure 313 reduce the optical fieldphase discontinuities in the Fraunhofer diffraction region, as shown inFIG. 68, without affecting the field amplitude. OPDs produced by thephase structure 313 result in coherent interactions between thefractions of radiation in the output plane 315 of the optical system310. FIGS. 69 and 70 show the three-dimensional intensity distributionsof the transformed field produced in the output plane 315 andcorresponding to different f-numbers of the optical system 310. Thef-number of the optical system 310 depends on the radial size of theoptical field within the Fraunhofer region, as well as the focal lengthsof the lenses 312 and 314. In accordance with the third embodiment, thef-number was adjusted by changing the radial size of the optical fieldwithin the Fraunhofer region. The optical field radial size was adjustedby changing the radial aperture size of the optical components 312, 313,or 314. FIG. 71 shows the relative axial cross-sections of theirradiance distributions produced in the output plane 315 for threedifferent field radii of 50.0 mm, 11.6 mm, and 8.0 mm. The threetransformed output field distributions shown in FIG. 71 containrespectively 94.5%, 93.5%, and 86.0% of the propagating radiation powerwithin the 15 microns diameter central node. The fractional powercontained within the central node of the transformed field significantlyexceeds the fractional power of 20.7% contained within the central nodeof the original PSF in the back focal plane of the optical system 300.

To increase the transformed field central node peak irradiance in theoutput plane 315, the phase structure 313 is comprised of an additionaldoughnut-shaped phase step, as shown in FIG. 72. The OPDs produced bythe phase structure 313 containing the additional doughnut-shaped phasestep further reduce the phase discontinuities of the modified fieldwithin the Fraunhofer diffraction region, as shown in FIG. 73. The OPDsproduced by the second phase structure 313 with the additionaldoughnut-shaped phase step further enhance constructive coherentinteractions between the fractions of radiation as they propagate to theoutput plane 315 of the optical system 310. FIGS. 74 and 75 showthree-dimensional intensity distributions of the transformed fieldproduced in the output plane 315 and corresponding to the respectivelens 314 aperture radii of 50.0 mm and 8.0 mm limiting the field in theFraunhofer diffraction region. FIG. 76 shows the relative axialcross-sections of the transformed field irradiance distributionsproduced in the output plane 315 for the three different lens 314limiting aperture radii of 50.0 mm, 11.6 mm, and 8.0 mm. The threeoutput field distributions shown in FIG. 76 contain respectively 94.9%,94.6%, and 87.1% of the radiation power within the 15 micron diametercentral node of the transformed field. FIG. 77 shows the relativeirradiance cross-sections of the transformed field distributionsproduced in the output plane 315 employing the lens 314 with a 50.0 mmlimiting aperture radius and the phase structure 313 with and withoutthe addition of the doughnut-shaped phase step, respectively. Theaddition of the doughnut-shaped phase step to the phase structure 313enhances the constructive coherent interactions between the fieldfractions in the output plane 315 and results in a 50% increase in thetransformed field peak irradiance.

The size of the central node of the transformed field produced in theoutput plane 315 is proportional to the phase step size of thediffractive structure 311 and to the absolute magnification value of theoptical system 310. The absolute magnification value, in turn, isproportional to the focal length f₂ of the lens 314, and is inverselyproportional to the focal length f₁ of the lens 312.

In the presence of wavefront distortions of the radiation propagatingthrough the optical system 300, the shape of the PSF produced in thefocal plane will also be distorted, as shown in FIGS. 11 and 12. Thefractions of propagating radiation contained within the central node ofthe distorted PSFs will be reduced as compared to the respectivefraction of the non-distorted PSF. FIGS. 78 through 81 present theintensity and phase distributions of the PSF produced in the focal planeof the optical system 300 in the presence of wavefront distortions ofthe incoming radiation. The field distributions shown in FIGS. 78 and 79correspond to the respective PSF irradiance and phase distributions inthe back focal plane of the optical system 300 in the presence of randomoptical path difference errors between the primary mirror segments 301through 306 ranging from −0.14λ to 0.15λ and listed in the second row ofTable 1. The field distributions shown in FIGS. 80 and 81 correspond tothe respective PSF irradiance and phase distribution in the back focalplane of the optical system 300 in the presence of random OPD errorsbetween the primary mirror segments 301 through 306, ranging from −0.35λto 0.21λ, and listed in the third row of Table 1. The fractional PSFpowers contained within the PSF central node in the presence of the OPDerrors listed in the second and third rows of Table 1 are 17.7% and12.9%, respectively.

Transformations of the distorted PSFs shown in FIGS. 78 through 81significantly increase the fractional power contained within the centralnode of the transformed output field in the output plane 315. Thefractional radiation power contained within the central node of thetransformed field depends on the lateral field size in the Fraunhoferdiffraction region. When the radial size of the field in the Fraunhoferregion is limited to 50.0 mm and the phase steps of the phase structures311 and 313 introduce localized optical path differences OPD=0.5.1, thetransformed output field contains within the 15 microns diameter centralzone approximately 78% of the radiation power for the phase distortionslisted in the second row of Table 1, and approximately 68% of theradiation power for the phase distortions listed in the third row ofTable 1.

An additional increase in the fractional radiation power containedwithin the central zone of the transformed output field, and theassociated increase in peak irradiance of the transformed field, can beachieved by adjusting the OPDs of the phase structures 311 and 313. Theincrease in the transformed field peak intensity and the fractionalpower contained within the central node of the transformed field isachieved by reducing the phase discontinuities between the differentfractions of the propagating field in the Fraunhofer diffraction region.This can be accomplished by employing electronically controlled highresolution spatial phase modulators (SPMs) in place of the phasestructures 311 and 313. The SPMs are controlled through a feedback loopby monitoring the fractional power contained within the central node ofthe field and by applying an optimization algorithm to maximize thefractional power. An optimization algorithm, known as StochasticParallel Gradient Descent (SPGD), was disclosed in the past to solvesimilar problems.

Table 3 shows the OPDs produced by the individual phase steps of thephase structure 313 employed to maximize the fractional power encircledwithin the 15 micron diameter central zone of the transformed field inthe output plane 315. The numerical notation for the individual phasesteps of the phase structure 313 in Table 3 is based on FIG. 9.

TABLE 3 Aperture Number 1 2 3 4 5 6 OPD set #1 (λ) 0.47 0.38 0.49 0.530.32 0.54 OPD set #2 (λ) 0.44 0.60 0.27 0.38 0.42 0.34

The maximum fractional power of the transformed field encircled within a15 micron diameter central zone in the presence of the random phaseerrors listed in the second row of Table 1 is achieved when the OPDproduced by the diffractive structure 311 phase step is adjusted toOPD=0.463.1 and the phase step OPDs of the phase structure 313 areadjusted to the values of OPD set #1 listed in Table 3. FIG. 82 presentsthe phase distribution in the Fraunhofer diffraction region locatedafter the lens 312 prior to the OPDs produced by the phase structure313. FIG. 83 presents the phase distribution in the Fraunhoferdiffraction region after the localized OPD modifications produced by thephase structure 313 corresponding to OPD set #1 listed in Table 3. Thedelays produced by OPD set #1 of the phase structure 313 reduce thephase discontinuities within the Fraunhofer diffraction region, as shownin FIG. 83, without affecting the field amplitude. For the lens 314 withan aperture radius of 50.0 mm, the 15 micron diameter central zone ofthe transformed field contains in the output plane 315 about 86.4% ofthe PSF power.

The maximum fractional power of the transformed field encircled within a15 micron diameter central zone in the presence of the random phaseerrors listed in the third row of Table 1 is achieved when the OPD ofthe phase step of the diffractive structure 311 is adjusted to 0.459λ,and the phase step OPDs of the second phase structure 313 are adjustedto the values of OPD set #2 listed in the third row of Table 3. FIG. 84presents the phase distribution of the radiation in the Fraunhoferdiffraction region produced prior to the phase structure 313. FIG. 85presents the phase distribution of the radiation in the Fraunhoferdiffraction region after the localized OPD modifications produced by thephase structure 313 corresponding to OPD set #2 listed in Table 3. Theoptical path differences produced by OPD set #2 of the phase structure313 reduce the phase discontinuities within the Fraunhofer region, asshown in FIG. 85, without affecting the field amplitude. For a lens 314with an aperture radius of 50.0 mm, the 15-micron diameter central zoneof the transformed field contains in the output plane 315 about 77.2% ofthe PSF power.

An increase in the transformed output field fractional power and thepeak intensity can also be achieved by minimizing the wavefrontdistortions of the propagating wavefront at the input of the opticalsystem 300. This is achieved by employing an additional phase structurewith spatially adjustable phase regions prior to the optical fieldentering the optical system 300. This phase structure can also becomposed of multiple phase regions controlled through a feedback loop byapplying an optimization algorithm.

Additional control over the shape of the transformed output field isachieved by employing diffractive phase structures 311 containingcomplex phase patterns that introduce OPDs to the optical field. FIGS.86 through 91 present the formation of the transformed output field withthree dominant peaks employing the diffractive structure 311 containingmultiple OPD regions. FIG. 86 presents a phase distribution of thediffractive structure 311 composed of three circular regions introducinglocalized OPDs and arranged into an equilateral triangular pattern withthe side lengths of 23 microns between the centers of the circularregions. The triangular pattern of the diffractive structure 311 iscentered with respect to the optical field produced in the focal planeof the optical system 300. The individual regions of the diffractivephase structure 311 are similar in shape to the circular phase patternshown earlier in FIG. 17, and have the radial size of 7.3 microns. Theregions of the phase structure shown in FIG. 86 produce an optical pathdifference of OPD=0.5λ to the optical field. FIG. 87 presents the phasedistribution of the optical field after modifications by the diffractivephase structure 311 containing the phase pattern shown in FIG. 86. FIGS.88 and 89 show the respective intensity and phase distributions of thefield diffracted by the phase structure 311 in the Fraunhoferdiffraction region prior to entering the second phase structure 313. Thesecond phase structure 313 contains six circular-shaped phase stepsarranged in a pattern shown in FIG. 67. The phase steps of the phasestructure 313 produce localized optical path differences of OPD=0.5λ andare oriented to match the hexagonal phase pattern in the Fraunhoferregion shown in FIG. 89. The radii of the individual phase steps of thephase structure 313 are 1.5 mm and are uniformly spaced in the azimuthaldirection, and the aperture centers are located on the circumference ofa circle with a radius of 5 mm. FIG. 90 shows the phase distribution inthe Fraunhofer diffraction region after phase modifications by the phasestructure 313. FIG. 91 shows the three-dimensional intensitydistribution of the transformed field in the output plane 315. Thethree-dimensional intensity distribution in FIG. 91 corresponds to a100.0 mm radial aperture size of the lens 314. The intensitydistribution of the transformed output field within the output plane 315contains three dominant intensity peaks arranged in a triangularpattern. The pattern of the peaks corresponds to the phase step patternof the diffractive structure 311 rotated by 180 degrees with respect tothe optical axis. The scale of the resulting pattern in the output plane315 depends on the magnification of the imaging optical system 310defined by the focal lengths of the lens components 312 and 314. Inaccordance with the third embodiment of the present invention, theimaging optical system 310 has a magnification of M=−1. Therefore, thethree output peaks of the transformed field are arranged into anequilateral triangular pattern with the peak centers spaced 23 micronsfrom each other. The three output peaks of the transformed field shownin FIG. 91 contain about 75% of the total PSF field power.

Amplitude diffractive structures can also be employed to perform fieldtransformations in accordance with the present invention. Although theuse of amplitude diffractive structures causes localized reduction intransmission of the field, and therefore leads to a reduction in powerof the transformed output field, the amplitude structures are oftensimpler to implement than the respective phase structures of a similarsize and shape. FIGS. 92 through 96 illustrate the case when anamplitude diffractive structure 311 obstructing a fraction of the PSFproduced by the optical system 300 is incorporated as a part of thetransforming optical system 310. The amplitude diffractive structure 311is centered with respect to the optical field produced in the back focalplane 315 of the optical system 310, and has a radius of 0.007 mm. FIG.92 presents the two-dimensional intensity distribution of the opticalfield in the back focal plane 315 after the localized field obstructionby the amplitude diffractive structure 311.

FIGS. 93 and 94 show the respective intensity and phase distributions inthe Fraunhofer diffraction region after diffraction by the firstamplitude structure 311 prior to entering the phase structure 313. Thephase structure 313 contains six circular-shaped phase steps arranged inthe pattern shown earlier in FIG. 67. The phase steps of the phasestructure 313 produce localized optical path differences of OPD=0.5λ andare oriented to match the hexagonal phase pattern in the Fraunhoferregion shown in FIG. 94. The radii of the individual phase steps of thephase structure 313 are 1.5 mm and the phase steps are uniformly spacedin the azimuthal direction with aperture centers located on thecircumference of a circle with a radius of 5 mm. FIG. 95 shows the phasedistribution in the Fraunhofer diffraction region after the phasemodifications produced by the phase structure 313. FIG. 96 shows thethree-dimensional intensity distribution of the transformed field in theoutput plane 315. The three-dimensional intensity distribution in FIG.96 corresponds to a 17.2 mm radial aperture size of the lens 314.Employment of the diffractive amplitude structure 311 reduces the fieldpower contained in the output plane 315 to 68% of the total power of thefocused field within the back focal plane of the optical system 300.Employment of the amplitude diffractive structure 311 and the phasestructure 313 results in the formation of a field in the output plane315 shown in FIG. 96. The central peak of the transformed field in FIG.96 contains about 44% of the total PSF field power. This is more thantwice higher than the fractional power contained within the central nodeof the original PSF in the back focal plane of the optical system 300,containing only 20.7% of the field power as shown in FIG. 10.

Fourth Embodiment

The optical system in accordance with the fourth embodiment of thepresent invention is designed to transform optical fields from multiplemutually coherent laser beams into far field distributions with enhancedfractional power contained in the far field central node. Multiplemutually coherent laser beams, known as optical phased arrays (OPAs),are often employed to increase the output laser power. OPAs may containa varying number of laser beams with different shapes and sizes, and maybe arranged into a variety of patterns, including linear, rectangular,circular, etc.

FIG. 97 presents the optical layout of the fourth embodiment of thepresent invention for producing transformed output field distributionsfrom OPAs. The layout in FIG. 97 contains an OPA 401, a phase structure402 incorporating several phase shifting elements inserted into thepaths of the OPA laser beams, a lens 403 with positive optical power fortransferring the OPA radiation into the far field, and an optical system410. The optical system 410 performs transformation of the OPA far fieldproduced by the lens 403 into a desired output field distribution. Theoptical system 410 contains a diffractive structure 404 in the form of aphase plate placed in the back focal plane of the lens 403, a lens 405with positive optical power located in proximity to the diffractivestructure 404, a phase structure 406 located in the back focal plane ofthe lens 405, and a lens 407 with positive optical power placed afterthe phase structure 406. To reduce the axial length of the opticalsystem 410, the lens 407 is placed in proximity to the phase structure406.

Although the lenses and the phase shifting components of the opticalsystem 410 are shown in FIG. 97 as refractive elements, reflective phasestructures producing optical path delays and mirrors can also beemployed instead of their refractive counterparts. The phase structurescan be fabricated lithographically onto lenses or mirror elements toreduce the number of individual components within the system. Refractiveor reflective electronically controllable spatial phase modulator arraysor individual electro-optical phase modulating elements capable ofdynamic adjustments of the OPDs may also be employed to produce therequired phase modifications to the optical fields.

The laser beams constituting the OPAs can be expanded and collimatedprior to reaching the array of phase shifting elements 402. The shapeand size of the OPA laser beams depends on the laser type and theproperties of the beam shaping, beam expanding, and collimating optics.For example, a coherent array of expanded and collimated beams maycontain a variety of beam shapes including Gaussian, super-Gaussian,top-hat, and doughnut-shaped beams. In accordance with the fourthembodiment, the OPA 401 contains seven Gaussian-shaped coherent laserbeams arranged in a pattern shown earlier in FIG. 13. Each Gaussian beamwithin the OPA 401 has a beam waist radius of 2.83 mm. The beam centersof the six peripheral Gaussian beams are located on the circumference ofa circle with a radius of 17 mm and are uniformly spaced at 60° angularincrements along the circle.

The incoming array of laser beams constituting the OPA 401 propagatesthrough the array of phase shifting elements 402 and the lens 403, andforms a far field distribution in the back focal plane of the lens 403.The phase shifting array 402 consists of seven individually addressablephase shifting elements with aperture diameters equal to 17 mm andcentered with respect to the centroids of the Gaussian laser beamsconstituting the OPA 401. The array of phase shifting elements 402 isarranged in a pattern shown in FIG. 98, where the phase shiftingapertures are individually labeled by numbers 1 through 7 to match therespective Gaussian beams of the OPA as identified in FIG. 13. The arrayof phase shifting elements 402 provides independent control of OPDsbetween the individual laser beams prior to propagation through the lens403. The phase shifting array 402 may be comprised of fastelectro-optical phase modulators for real-time compensation of relativeOPD fluctuations between the individual laser beams within the OPA 401.

A three-dimensional irradiance distribution of the focused OPA far fieldproduced in the back focal plane of the focusing lens 403, when the OPDsbetween the individual laser beams within the OPA are zero, was shown inFIG. 14. FIG. 99 shows a two-dimensional irradiance distribution of thefocused OPA far field that corresponds to the three-dimensionaldistribution in FIG. 14. Similar far field shapes and sizes will beproduced when the OPDs between the individual laser beams are equal toan integer number j of the emission wavelength OPD=jλ. In the trivialcase of j=0, the optical path difference OPD=0, and the individual laserbeams of the OPA are in phase. In accordance with the fourth embodiment,the focal length of the focusing lens 403 is f₁=1000 mm and thewavelength of the radiation is 0.55 microns. The central node of the farfield distribution produced in the back focal plane of the opticalelement 403 has a radial size of 0.014 mm and contains 55.8% of thetotal OPA power. The side lobes of the far field contain the remaining44.2% of the OPA power.

The diffractive structure 404 of the optical system 410 is placed in theback focal plane of the lens 403. The structure 404 diffracts a fractionof the OPA far field in the focal plane of the lens 403 by employingphase patterns that produce localized optical path discontinuities. Thediffractive structure 404 may contain a variety of phase patterns,including the patterns shown in FIGS. 16 through 23.

In accordance with the fourth embodiment, the diffractive phasestructure 404 contains a single circular-shaped phase step, similar tothe phase pattern shown in FIG. 17. The fourth embodiment is designed toincrease the fractional power within the central node of the transformedOPA field by coupling a fraction of the far field side lobe power intothe central node of the transformed field. The higher fractional powerswithin the central node of the transformed field can be achieved whenthe size of the phase step of the diffractive structure 404 does notexceed the size of the central node of the focused far field in the backfocal plane of the lens 403. In accordance with the specificimplementation, the phase structure 404 contains a circular-shaped phasestep with a radial size of 0.007 mm centered with respect to the centralnode of the focused OPA irradiance distribution produced in the backfocal plane of the lens 403. FIG. 100 shows the phase distribution ofthe focused OPA far field modified by the diffractive phase structure404. The circular-shaped phase step of the phase structure 404 producesan optical path difference OPD=0.5λ to the focused OPA field. When thephase step of the diffractive structure 404 is fabricated as a phaserelief pattern, the height of the phase steps h within the phasestructure substrate is calculated based on equation (3). For thediffractive structure 404 made from BK7 glass with a refractive indexn=1.5185 at the wavelength of λ=0.55 micron, the step height hcorresponding to OPD=0.5λ equals 0.53 microns.

In high power laser applications, the power density within the centralnode of the focused far field distribution in the back focal plane ofthe optical element 403 may exceed the damage threshold of thediffractive structure 404 coatings or the substrate material. To preventthe radiation damage of the diffractive structure 404, the structure 404is designed to contain a central opening that equals the size of thecentral phase step. In accordance with the fourth embodiment, thediffractive structure 404 contains a central opening with a radial sizeof 0.007 mm, and is shown in FIG. 101. The opening is centered withrespect to the central node of the far field produced within the backfocal plane of the lens 403. The substrate thickness t of the phasestructure 404 is adjusted to produce a controlled OPD to the fraction ofthe radiation propagating through the substrate. The thickness t iscontrolled to produce an OPD equal to an odd integer number j of halfthe wavelengths of the radiation OPD=t*(n−1)=jλ/2, where n is therefractive index of the substrate material. The phase structure 404 ismade from BK7 glass with a refractive index n=1.5185 at a wavelength ofλ=0.55 microns and has a substrate thickness of 0.340 mm. The phasestructure 404 produces OPD=0.176 mm to the OPA radiation with respect tothe fraction of radiation propagating through the central opening,corresponding to an integer value of half the wavelengths j=641.

The OPA far field diffracted by the phase structure 404 is furthermodified by the lens 405 with positive optical power located inproximity to the structure 404. FIG. 102 shows irradiance distributionof the diffracted field in the Fraunhofer diffraction region in the backfocal plane of the lens 405. The phase structure 406 is located in theback focal plane of the lens 405 where the Fraunhofer diffractionpattern is produced. The phase structure 406 produces controlled OPDs tofractions of the OPA field in the Fraunhofer diffraction region thatresult in coherent interactions within the propagating field.

The phase structure 406 contains seven circular-shaped phase steps asshown in FIG. 103. The radius of the central phase step of the phasestructure 406 is equal to 0.51 mm, and the radii of the outer phasesteps of the phase structure 406 arranged in the hexagonal pattern areequal to 0.60 mm. The phase step centers of the phase structure 406 areuniformly spaced on the circumference of a circle with radius 1.738 mm.The phase steps of the phase structure 406 introduce localized opticalpath differences of OPD=0.5λ to the field within the Fraunhofer region.For a wavelength of the propagating radiation λ=0.55 micron and thephase structure substrate made of BK7 glass, the height h of the phaserelief steps is equal to 0.53 microns. FIG. 104 shows the phasedistribution at the output of the phase structure 406. The OPDs producedby the phase steps of the phase structure 406 are designed to reduce thephase discontinuities of the optical field in the Fraunhofer region, asshown in FIG. 104.

A second lens 407 with positive optical power is located in the vicinityof the phase structure 406. In accordance with the fourth embodiment,the focal lengths of the lenses 405 and 407 are equal to each otherf₂=f₃=100 mm. The transformed output field is produced in the far fieldwith respect to the lens element 407. The shape of the transformed fieldproduced at the output of the lens 407 depends on the lateral size ofthe field propagating through the lens 407. The lateral size of thefield at the output of the lens 407 can be controlled by placing alimiting aperture within the field. FIGS. 105 and 106 presentthree-dimensional output radiance distributions for the lens 407aperture radii of 12.7 mm and 8.7 mm, respectively. FIG. 107 shows therelative cross-sections of the output radiance distributions for threerespective lens 407 aperture radii of 12.7 mm, 8.7 mm, and 5.3 mm. Thethree output far field distributions shown in FIG. 107 contain withintheir respective central nodes 77%, 75%, and 70% of the total OPA power,respectively. The fractional power within the central node of thetransformed output radiation exceeds the fractional power within thecentral node of the OPA far field produced in the back focal plane ofthe lens 403, which contained 55.8% of total OPA power.

Fifth Embodiment

The optical system in accordance with the fifth embodiment of thepresent invention is designed to transform far field distributions frommultiple mutually coherent laser beams comprising an OPA into far fielddistributions with enhanced fractional power contained within the fieldcentral node. The transformed far field distribution is produced at aspecific working distance from the optical system.

FIG. 108 presents the layout of the optical system in accordance withthe fifth embodiment of the present invention. It contains an array ofcollimated incoming laser beams 501 comprising the OPA, a phasestructure 502 for adjusting phase distributions of the collimated OPAbeams, an optical system 500 with positive optical power for producingthe OPA far field in the back focal plane, and an optical system 520 fortransforming the OPA far field.

The OPA 501 in accordance with the fifth embodiment is comprised ofseven Gaussian-shaped coherent laser beams arranged in the beam patternshown earlier in FIG. 13. Each Gaussian beam within the OPA 501 has abeam waist radius of 2.83 mm and a wavelength of 0.55 micron. The 6peripheral Gaussian beams are located on the circumference of a circlewith a radius of 17 mm. The Gaussian beam centers are uniformly spacedat 60 degree angular increments in the azimuthal direction. The incomingarray of laser beams 501 propagates through the diffraction-limitedoptical system 500, and forms the far field distribution in the backfocal plane of the optical system 500. The phase structure 502 is placedprior to the optical system 500 to adjust the wave fronts of the OPAbeams, as well as OPDs between the individual beams comprising the OPA.

The lens system 500 shown in FIG. 108 is designed to have a compactaxial size with a long effective focal length intended to reduce the farfield power density at the phase element 505 below its damage threshold.The effective focal length of the lens system 500 is longer than theaxial length of the lens system. The optical system 500 is composed of afirst lens element 503 with positive optical power and a second lenselement 504 with negative optical power spaced along the optical axis,and has an effective focal length of 1000 mm. The first lens element 503has a focal length of 68.00 mm and the second lens element 504 has afocal length of −14.59 mm. The lens elements 503 and 504 are spaced54.40 mm along the propagation direction. The back focal plane of thecomposite lens 500 is located 200.00 mm after the second lens element504. The axial distance from the first lens element 503 of the opticalsystem 500 to the back focal plane is equal to 254.40 mm, and isapproximately four times shorter than the effective focal length of thecomposite lens system 500.

When the wavefront distortions and OPDs of the laser beams comprisingthe OPA 501 are compensated for by the phase structure 502, the farfield intensity distribution in the back focal plane of thediffraction-limited optical system 500 contains a central node with aradius of 0.014 mm and 55.8% of the OPA power. The remaining 45.2% ofthe far field OPA power is contained within the numerous radiation nodesdiffracted outside of the central node. In the presence of the wavefront distortions and random OPDs between the OPA beams, the shape ofthe far field distribution in the back focal plane of the lens system500 will be distorted. FIG. 109 shows the irradiance distributionproduced in the back focal plane of the optical system 500 in thepresence of random OPDs between the individual laser beams. The fielddistribution in FIG. 109 corresponds to random phase errors between theOPA beams ranging from −0.35λ to 0.21λ as listed earlier in Table 2. Thefractional of the OPA power within the central node of the distorted OPAfar field is reduced to 40.6%, while the fraction of the OPA powerwithin the radiation diffracted outside of the central node is increasedto 59.4%.

The optical system 520 modifies the OPA far field in the back focalplane of the optical system 500, and produces the transformed fielddistribution in the output plane 510. The optical system 520 contains adiffractive phase structure 505 placed into the far field in thevicinity of the back focal plane of the composite lens 500, a lens 506with positive optical power for producing a Fraunhofer diffraction ofthe far field diffracted by the structure 505, a phase structure 507placed after the lens 506 into the Fraunhofer diffraction field, a lens508 with positive optical power that follows the phase structure 507,and an output plane 510 located in the back focal plane of the lens 508.

The spacing between the optical components 506, 507, and 508 is selectedbased on the optical layout considerations. When the phase structure 507is refractive, the lens 508 can be placed in proximity to the phasestructure 507 to reduce the axial size of the system, as shown in FIG.108. If the phase structure 507 is made reflective, axial separationbetween the phase structure 507 and the lens 508 will be required toprevent field obstruction by the lens aperture. The optical elements506, 507, and 508 can also be combined into a single optical componentthat incorporates the functions of the combined elements.

The phase structure 505 diffracts a fraction of the far field byproducing localized OPDs within the OPA far field. The diffractedoptical field further propagates through the lens element 506 with apositive optical power located at the front focal distance from thephase structure 505. The lens 506 modifies the wavefront curvature ofthe diffracted field and produces a Fraunhofer diffraction pattern ofthe field modified by the phase structure 505. The phase structure 507modifies the Fraunhofer diffraction pattern produced by the lens 506 byproducing controlled OPDs to the localized fractions of the field in theFraunhofer region. The modified field is further directed onto the lens508 with a positive optical power. The lens 508 modifies the wavefrontcurvature of the field 509 and produces the transformed optical field inthe output plane 510 based on coherent interactions between thediffracted and non-diffracted fractions of the OPA field.

The phase structure 505 diffracts the far field by producing an OPD to afraction of the OPA far field central node. In accordance with the fifthembodiment, the phase structure 505 contains a circular-shaped phasestep with a radial size of 0.011 mm centered with respect to the centralnode of the far field in the back focal plane of the optical system 500.The circular-shaped phase step produces an optical path differenceOPD=0.5λ to a fraction of the focused OPA field. For the phase structure505 made from BK7 glass with a refractive index of n=1.5185 and anoperating wavelength of λ=0.55 micron, the step height h correspondingto the OPD=0.5λ equals 0.53 microns based on equation (3). FIG. 110presents the phase distribution at the back focal plane of the opticalsystem 500 after propagation through the phase structure 505.

FIGS. 111 and 112 present the respective OPA field irradiance and phasedistributions in the Fraunhofer diffraction region produced at thesurface of the phase structure 507 after the lens 506. The phasestructure 507, in accordance with the fifth embodiment, is composed of alarge number of localized transparent phase cells with individuallyadjustable phases. The localized cells of the phase structure 507produce localized OPD adjustments within the optical field in theFraunhofer diffraction region. To maximize the fractional filed powercontained within the central node of the transformed field, the phasestructure 507 minimizes phase discontinuities within the Fraunhoferdiffraction region, resulting in a uniform phase distribution across thefield. FIG. 113 presents the phase distribution of the field in theFraunhofer region after OPD adjustments by the phase structure 507. Thereduction in phase discontinuities in the Fraunhofer region can beachieved by controlling the individual localized phase cells of thephase structure 507 through a feedback loop employing optimizationalgorithms, such as the Stochastic Parallel Gradient Descent (SPGD)algorithm.

The lateral size of the transformed field central node produced in theoutput plane 510 is proportional to the lateral size of the phase stepof the diffractive structure 505 and magnification of the system 520defined as a ratio of the focal lengths f₅₀₈/f₅₀₆ of the lens elements508 and 506. The central node size of the transformed field in theoutput plane 510 can be adjusted based on the appropriate selection ofthe focal lengths of the lens elements 506 and 508. When the focallengths of the lens elements 506 and 508 are equal, i.e. when f₅₀₆=f₅₀₈,the lateral size of the central node of the transformed field in theoutput plane 510 is equal to the lateral size of the phase step producedby the phase structure 505. FIG. 114 presents the two-dimensionaltransformed OPA irradiance distribution within the output plane 510 thatcorrespond to the uniform phase distribution of the modified field inFIG. 113. The phase distribution in FIG. 114 contains 83.5% of the OPApower within the central node of the transformed field with a 0.011 mmradius.

Field modifications by the phase structure 507 can also be employed tocontrol the lateral position of the transformed output field in theoutput plane 510, as shown in FIGS. 115 through 117. FIG. 115 presentsan exemplary phase distribution produced by the second phase structure507 in the Fraunhofer region. The localized OPDs produced by the cellsof the phase structure 507 within the Fraunhofer region result in aphase gradient across the optical field, as shown in FIG. 115. Changesin the magnitude and direction of the phase gradient will result inrespective changes in the magnitude and direction of the transformedfield displacement within the output plane 510. FIGS. 116 and 117present the respective two-dimensional and three-dimensional irradiancedistributions of the transformed field in the output plane 510corresponding to the phase gradient shown in FIG. 115. The lateral shiftof the central node within the output plane 510, as shown in FIGS. 116and 117, is a result of the phase modifications produced by the secondphase structure 507.

What is claimed is:
 1. A system for coherent transformation of opticalfields, the system comprising: an optical system with positive opticalpower for producing a far field distribution of the optical field; adiffractive structure located within the far field distribution of saidoptical field and containing spatially localized features fordiffracting fractions of the far field distribution; an opticalcomponent with positive optical power located within the fielddiffracted by said diffractive structure, said optical componentproducing a Fraunhofer diffraction field, a phase structure locatedwithin the produced Fraunhofer diffraction field and containing aspatially localized phase pattern, said phase pattern producing opticalpath differences to spatially localized fractions of the Fraunhoferdiffraction pattern.
 2. The system in accordance with claim 1, whereinthe focal length of the optical system producing the far fielddistributions exceeds the focal length of the optical component withpositive optical power for producing the Fraunhofer diffraction pattern.3. The system in accordance with claim 1, wherein lateral dimensions ofthe spatially localized features of the diffractive structure aresmaller than the central node size of the far field distribution.
 4. Thesystem in accordance with claim 1, wherein the diffractive structureincludes localized features that are spatially adjustable.
 5. The systemin accordance with claim 1, wherein the diffractive structure includesfeatures that produce at least one of localized amplitude modificationsand phase modifications within the far field.
 6. The system inaccordance with claim 5, wherein the diffractive structure includesspatially localized features with optical path delays equal to jλ2, forwhich j is an odd integer number and λ is the wavelength.
 7. The systemin accordance with claim 5, wherein the diffractive structure includesspatially adjustable localized features
 8. The system in accordance withclaim 1, wherein the diffractive structure is located at a front focaldistance from the optical component with positive optical power.
 9. Thesystem in accordance with claim 8, wherein an additional opticalcomponent with positive optical power is located within the far fielddistribution produced by said optical system.
 10. The system inaccordance with claim 9, wherein the focal lengths of the opticalcomponents with positive optical power are equal.
 11. The system inaccordance with claim 9, wherein the optical component with positiveoptical power and the diffractive structure are combined into a singleoptical component.
 12. The system in accordance with claim 1, whereinthe phase structure located within the Fraunhofer diffraction regionincludes a spatially localized phase pattern with adjustable opticalpath differences.
 13. The system in accordance with claim 1, wherein thephase structure located within the Fraunhofer diffraction regionincludes a spatially localized phase pattern with optical pathdifferences equal to jλ/2, where j is an odd integer number and λ is theradiation wavelength.
 14. The system in accordance with claim 1, whereinthe phase structure includes a spatially localized phase pattern locatedwithin the Fraunhofer diffraction region.
 15. The system in accordancewith claim 16, wherein said optical component and the phase structureare combined into a single optical element.
 16. The system in accordancewith claim 1, wherein the phase structure includes a spatially localizedphase pattern located within the Fraunhofer diffraction region in theback focal plane of the optical component with positive optical power.17. The system in accordance with claim 1, further comprising a meansfor limiting the lateral size of the optical field within the Fraunhoferdiffraction region.
 18. The system in accordance with claim 1, furthercomprising an additional optical component with positive optical powerlocated in the optical field within the Fraunhofer diffraction field.19. The system in accordance with claim 18, wherein the opticalcomponent with positive optical power and the phase structure arecombined into a single optical element with equivalent optical power andphase characteristics.
 20. The system in accordance with claim 21,wherein the observation plane including the transformed optical field islocated in the back focal plane of said additional optical component.21. The system in accordance with claim 1, further comprising anadditional phase structure with spatially localized features withadjustable optical path delays, and said additional phase structurelocated in the path of the input optical field prior to the opticalsystem with positive optical power for producing the far fielddistribution of the input optical field.